Programme Learning Outcomes in B.Sc. Statistics 1. 2. 3. 4....SARDAR PATEL UNIVERSITY B.SC. SYLLABUS STATISTICS SEMESTER – III Effective from June, 2019 Sr. No. Course code Title

Programme Learning Outcomes in B.Sc. Statistics

The student graduating with the Degree B.Sc. Statistics should be able to:

1. Demonstrate the ability to use Statistics knowledge to identify and apply appropriate

methodologies to solve a wide range of problems associated with Statistics.

2. Plan and execute Statistical experiments or investigations, analyze and interpret data

collected using appropriate methods and appropriate statistical software, and prepare a

report of the findings of the experiment/investigations.

3. Find employment utilizing his/her appropriate statistical skill in interdisciplinary areas

such as finance, insurance, health, agriculture, government, business, industry,

telecommunication, and bio-statistics. Consequently, they can pursue their future career

either in the core field or in the applied field of Statistics.

4. Use his/her appropriate statistical skill in interdisciplinary areas such as finance, health,

agriculture, government, business, industry, telecommunication, and bio-statistics. As a

result, they can pursue their future career either in the core field or in the applied field of

Statistics.

SARDAR PATEL UNIVERSITY

B.SC. SYLLABUS

STATISTICS

SEMESTER – III

Effective from June, 2019

Sr. No. Course code Title of the paper

Credit Lecture per week/batch

Core/Skill Enhancement

1 US03CSTA21 Descriptive Statistics

4 4 Core

2 US03CSTA22 Elements of Probability

Theory

4 4 Core

3 US03CSTA23 Statistics Practical - I

4 8 Core

4 US03SSTA21 Foundation of Statistics - I

2 2 Skill Enhancement

5 US03SSTA22 Operations Research-I

2 2 Skill Enhancement

6 US03SSTA23 Biostatistics - I 2 2 Skill Enhancement


Vallabh Vidyanagar, Gujarat

(Reaccredited with ‘A’ Grade by NAAC (CGPA 3.25) Syllabus with effect from the Academic Year 2021-2022

Page 1 of 3

(Bachelor of Science in Statistics) (Bachelor of Science)

(B. Sc.) (Statistics) Semester (III)

Course Code US03CSTA51

Title of the

Course DESCRIPTIVE STATISTICS

Total Credits

of the Course 04

Hours per

Week 04

Course

Objectives:

1. To understand the purpose of descriptive statistics

2. To compute various measures of central tendency, dispersion with its

merits and demerits and its usefulness in real life.

3. To explain the problems arising in the construction of index numbers,

importance of an index numbers.

4. To perform basic demographic analyses using various techniques.

5. To learn the main theories used to understand population studies.

Course Content

Unit Description Weightage*

(%)

1. Analysis of Quantitative data - I

Types of data : Quantitative data : Discrete and Continuous,

Qualitative data : Nominal and Ordinal

Measures of central tendency : Mean, Median, Mode, Geometric mean,

Harmonic mean, Weighted mean, Combined mean, Merits & demerits,

Properties (with proof), Real life examples

25

2. Analysis of Quantitative data - II

Partition values and their graphical representation

Measures of Dispersion : Range, Quartile derivation, Mean Derivation,

Standard derivation, Coefficient of variation(C.V), Merits & Demerits,

Properties (with proof), Box – and – whisker plot, Lorenz curve, Stem

– and – Leaf diagram

Moments : Raw moments, Central moments, Relationship between raw

and central moments, Skewness, Kurtosis, Real life examples

25

3. Index numbers : Introduction, Uses of index number, Steps for

construction of index numbers, Problems in the construction of index

numbers, Methods of constructing index numbers, Simple

(Unweighted) Aggregate method, Weighted Aggregate method,

25




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Laspeyre’s Price Index, Paasche’s Price Index, Fisher’s Price Index,

Marshall Edgeworth Price Index, Tests of consistency of Index

number, Time reversal test, Factor reversal test

4. Vital Statistics :

Uses of Vital statistics and methods of collecting vital statistics

Measurement of Mortality: Crude Death Rate (CDR), Specific Death

Rate (SDR), Standardized Death Rate (STDR)

Measurement of Fertility: Crude Birth Rate (CBR), General Fertility

Rate (GFR), Specific Fertility Rate (SFR), Total Fertility Rate (TFR)

Measurement of population growth, Methods of measuring population

growth, Crude rate of natural increase, Vital index, Gross

Reproduction Rate (GRR)

25

Teaching-

Learning

Methodology

Evaluation Pattern

Sr.

No.

Details of the Evaluation Weightage

1. Internal Written / Practical Examination (As per CBCS R.6.8.3) 15%

2. Internal Continuous Assessment in the form of Practical, Viva-voce,

Quizzes, Seminars, Assignments, Attendance (As per CBCS R.6.8.3)

15%

3. University Examination 70%

Course Outcomes: Having completed this course, the learner will be able to/impart

1. Understand the fundamental statistics concepts and its applications and to organize,

manage and present the data.

2. Knowledge of various types of data, their organization and evaluation of summary

measures such as measures of central tendency and dispersion.




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3. Understand the uses of index numbers, Unweighted and weighted index numbers.

4 Commonly used measures of demography pertaining to its three basic aspects, viz, the

mortality, and fertility and population growth.

Suggested References:

Sr.

No.

References

1. Gupta S.C. : Fundamentals of Statistics

2. Gupta S.C. : Fundamentals of Applied Statistics

3 Gupta S.C. and V.K.Kapoor : Fundamentals of Mathematical Statistics

4 Agarwal B.L. : Basic statistics

On-line resources to be used if available as reference material

On-line Resources

*****




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Course Code US03CSTA52 Title of the

Course

ELEMENTS OF PROBABILITY

THEORY

Total Credits

of the Course 04

Hours per

Week 04

Course

Objectives:

1. Understand the basic principles of probability including the set theory,

conditional probability, Bayes’ theorem and its applications in real life

problems.

2. Distinguish between independent and correlated random variables.

3. Distinguish between discrete, continuous and mixed random variables

and be able to represent them using probability mass, probability density

and cumulative distribution functions.

Course Content


(%)

1. Probability : Concept of Set theory, Permutation & combination,

Random experiment , sample space, Events, Types of sample space,

Meaning and definition of probability - classical & axiomatic, Laws of

probability (with proof), Conditional probability and independent

events, Law of total probability, Bayes’ theorem, Examples

25

2. Random variables and probability distribution : Random variable,

Types of r.v : Discrete and Continuous, Probability mass function

(p.m.f), Probability density function (p.d.f), Distribution function

(c.d.f), Median, mode and partition values

25

3. Mathematical Expectation: Definition, Properties (with proof),

Moments, measures of central tendency, dispersion, skewness and

kurtosis, Moments and Generating functions (non - standard

distributions), Probability generating function (p.g.f), moment

generating function (m.g.f.) and its properties, cumulant generating

function(c.g.f.)

25

4. Bivariate distribution :Joint, marginal and conditional p.m.f of two

random variables, Joint, marginal and conditional p.d.f of two random

25




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variables, Independence of two random variables (examples-

nonstandard distribution), Product moments, Correlation, Conditional

mean and variance

Teaching-

Learning

Methodology

Evaluation Pattern

Sr.

No.





15%


Course Outcomes: Having completed this course, the learner will be able to

1. Use the basic probability rules, including additive and multiplicative laws, using the

terms, independent and mutually exclusive events.

2. Acquire knowledge related to concept of discrete and continuous random variables and

their probability distributions including mathematical expectations and moments


Sr.

No.

References

1. Gupta S.C. and Kapoor V.K. : Fundamentals of Mathematical Statistics

2. Mood A.M. and Graybill F.A. and Boes D.C.E.: Introduction to theory of statistics




Page 3 of 3

3 Hogg and Craig: Introduction to Mathematical Statistics

4 Biswas Purna Chandra: Probability & Statistics (PHI Edition)


On-line Resources

*****




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Course Code US03SSTA51

Title of the

Course FOUNDATION OF STATISTICS - I

Total Credits

of the Course 02

Hours per

Week 02

Course

Objectives:

The main objective of this course is to acquaint students with some basic

concepts in Statistics. They will be introduced to some elementary statistical

methods of analysis of data. At the end of this course students are expected

to be able to analyse the data.

Course Content


(%)

1. Collection of data – I: Introduction, meaning, applications and

limitations of Statistics, Methods of collecting data : Survey Method

and Experimental method, Concept of a statistical population and

sample from a population, Advantages of sample survey, Methods of

sampling: Simple random sampling, Stratified random sampling,

Systematic sampling

25

2. Collection of data – II: Primary data, Methods of collecting primary

data: Direct personal inquiry method, Mailed Questionnaire method,

Indirect oral investigation method, Secondary data, Chief sources of

secondary data, Difference between Primary and Secondary data,

Types of characteristics (data), Attributes: Nominal and Ordinal,

Variables: Discrete and Continuous

25

3. Presentation of data: Classification: Definition, Purpose, Rules and

Types of classification, Tabulation: Meaning & importance, Parts of a

table, Requisites of good table, Types of table, Simple or one way

table, Two way table, Manifold table (Up to four) (with examples),

Diagrammatic and Graphical presentation of data: Importance and its

uses, Types of diagrams, Bar diagram: Simple, Sub-divided,

Percentage, Multiple, Pie chart, Graphical presentation of data:

Histogram (with uniform class-width),Frequency polygon, Frequency

25




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curves, Ogives, Determination of median and mode from graphs

4. Analysis of Quantitative data: Measures of central tendency (Mean,

Median, Mode), Measures of dispersion: Range, Quartile Deviation,

Standard Deviation and Coeff. of Variation, Skewness (Bowley’s and

Karl-Pearson’s coeff. of skewness)

25

Teaching-

Learning

Methodology

Evaluation Pattern

Sr.

No.





15%



1. tabulate statistical information given in descriptive form

2. use graphical techniques and interpret

3. compute various measures of central tendency, dispersion, skewness

4 apply statistics in the various fields.





Page 3 of 3

Sr.

No.

References

1. Gupta S.C. and Kapoor V.K. : Fundamentals of applied statistics

2. Gupta S.C. : Fundamentals of statistics

3 Ken Black, Business Statistics (4th

edition ) Willey student edition


On-line Resources

*****




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Title of the

Course OPERATIONS RESEARCH - I

Total Credits

of the Course 02

Hours per

Week 02

Course

Objectives:

1. To impart knowledge in concepts and tools of Operations Research

2. To formulate verbal problem into mathematical form

3. To understand mathematical tools that are needed to solve optimization

problems used in Operations Research

4. To apply techniques constructively to make effective business

decisions.

Course Content


(%)

1. Linear Programming – I: Introduction, Formulation of LPP,Solution of

LPP using Graphical method

25

2. Linear Programming – II: Solution of LPP using Simplex method ( Big

M method), Duality

25

3. Transportation Problems – I: Introduction, Mathematical formulation

of Transportation problem, Methods of finding i.b.f. solution: North

West Corner Method (N-W Corner Method), Row Minima Method,

Column Minima method, Matrix Minima Method ( Least Cost Entry

Method), Vogel’s Approximation method (VAM)

25

4. Transportation Problems – II: uv method of obtaining optimum

solution of TP, Unbalanced TP, Degenerate TP

25

Teaching-

Learning

Methodology




Page 2 of 3

Evaluation Pattern

Sr.

No.





15%



1. solve Linear Programming problems using various methods

2. solve Transportation Problems and its applications in day to day life.


Sr.

No.

References

1 KantiSwarup Gupta, P.K. and Manmohan : Operations Research, Sultan Chand and

Sons

2. Sharma J.K. : Operations Research

3 Taha Hamdy A. : Operations Research


On-line Resources




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*****




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Title of the

Course BIOSTATISTICS - I

Total Credits

of the Course 02

Hours per

Week 02

Course

Objectives:

1. Understand and apply statistical methods for the design of

experiments.

2. To recognize the importance of data collection and presentation.

3. Apply descriptive measures used to summarize data.

4. Understand the basic concepts of probability theory to learn concepts

of testing of hypothesis.

Course Content


(%)

1. Collection and Presentation of data: Variables used in biology

Collection and tabulation of quantitative and qualitative data,

Diagrammatic representation of data: Bar Diagram : Simple, Sub-

divided (Component), Percentage, Multiple, Pie Chart

Graphical representation of data: Histogram, frequency polygon,

frequency curves, Ogives, Determination of median and mode from

graph

25

2. Analysis of Quantitative data – I: Measures of central tendency, Mean,

Median, Mode, Partition values, Applications in the field of

Biosciences

25

3. Analysis of Quantitative data – II: Measure of dispersion, Range,

Quartile deviation (Q.D), Standard deviation (S.D), Coefficient of

Variation (C.V), Skewness, Karl-Pearson’s coefficient of skewness,

Bowley’s coefficient of skewness

25

4. Introduction to probability: Basic concepts of probability, Various

definitions of probabilities, Laws of probabilities and Examples,

Discrete Probability Distributions: Binomial, Poisson and Examples

25




Page 2 of 3

Teaching-

Learning

Methodology

Evaluation Pattern

Sr.

No.





15%



1. Define the principal concepts about biostatistics

2. Collect data relating to variable/variables which will be examined and calculate

descriptive statistics from these data.

3. Present the data through various graphs and diagrams

4 Apply the concepts of probability and discrete probability distributions applied in the

field of bioscience.


Sr.

No.

References

1. Gupta S.C : Mathematical Statistics

2. Mahajan B.K. : Methods in Biostatistics

3 Sancheti D.C. and Kapoor V.K. : Statistics




Page 3 of 3

4 Wayne W. Daniel : Biostatistics - A foundation for analysis in the health sciences


On-line Resources

*****


B.SC. SYLLABUS

STATISTICS

SEMESTER – IV

Effective from June, 2019

Sr. No. Course code Title of the paper Credit Core/Foundation/Elective

1 US04CSTA21 Statistical Techniques

4 Core

2 US04CSTA22 Probability Distributions

4 Core

3 US04CSTA23 Statistics Practical - II

4 Core Practical

4 US04SSTA21 Foundation of Statistics - II

2 Skill Enhancement

5 US04SSTA22 Operations

Research - II

2 Skill Enhancement

6 US04SSTA23 Biostatistics - II 2 Skill Enhancement




Page 1 of 3


(B. Sc.) (Statistics) Semester (IV)


Title of the

Course STATISTICAL TECHNIQUES

Total Credits

of the Course 04

Hours per

Week 04

Course

Objectives:

1. To study causal relationship between two related variables and measure

the strength of relationship between two variables.

2. Understand the line of best fit as a tool for summarizing a linear

relationship and predicting for the future.

3. To provide basic idea and tools of Statistical Quality Control

4. Understand the fundamental advantage and necessity of forecasting in

various situations

Course Content


(%)

1. Curve fitting: Principle of least squares, Fitting of 𝑖 𝑌 = 𝑎 + 𝑏𝑋

𝑖𝑖 𝑌 = 𝑎 + 𝑏𝑋 + 𝑐𝑋2 𝑖𝑖𝑖 𝑌 = 𝑎𝑏𝑋 𝑖𝑣 𝑌 = 𝑎𝑋𝑏 ,Correlation,

Objectives, Definition, Methods of studying correlation, Scatter

diagram method, Karl- Pearson’s correlation coefficients and its

properties (with proof), Spearman’s Rank Correlation coefficient and

its properties (with proof), Examples

25

2. Multiple, Partial correlation (for 3 variables only) and Regression,

Multiple correlation, Partial correlation, Examples, Regression,

Meaning and importance, Derivation of both the regression lines and

properties of regression coefficients (with proof), Examples, Multiple

linear regression with two independent variables

25

3. Time series Analysis: Components, Additive and Multiplicative

models, Calculation of trend using, Free hand curve, Semi averages

method, Moving average, Least squares method, Calculation of

seasonal indices using, Simple Average, Ratio to Trend, Ratio to

Moving Average, method

25




Page 2 of 3

4. Statistical Quality Control (SQC): Introduction, Types of Control

charts, For Variables: X and 𝑅 Charts, For Attributes: 𝑝, 𝑛𝑝 and 𝐶

charts

25

Teaching-

Learning

Methodology

Evaluation Pattern

Sr.

No.





15%



1. learn how to apply linear regression models in practice

2. understand and interpret the correlation between two variables

3. understand the importance and components of time series and measures to analyse time

series data.

4 understand the basic concepts of quality, quality control and tools to improve quality

5 demonstrate the ability to use and interpret control charts for variables and attributes


Sr. References




Page 3 of 3

No.

1. Gupta S.C. and Kapoor V.K. Fundamentals of applied statistics

2. Ken Black, Business Statistics (4th

edition ) Willey student edition

3 Gupta S.C, Fundamentals of statistics by S.C. Gupta

4 Douglas C. Montgomery : Introduction to Statistical Quality Control Wiley student edition


On-line Resources

*****




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Title of the

Course PROBABILITY DISTRIBUTIONS

Total Credits

of the Course 04

Hours per

Week 04

Course

Objectives:

1. To study various discrete and continuous probability distributions and

its applications in various real life situations.

2. To identify the appropriate probability model that can be used.

Course Content


(%)

1. Discrete probability distributions: Bernoulli distribution, Binomial

distribution, Poisson distribution, Geometric distribution, Negative

binomial distribution, Hyper geometric distribution, Discrete uniform

distribution, Mean variance, m.g.f, p.g.f and c.g.f. and its applications

25

2. Continuous probability distributions: Continuous uniform distribution,

Normal distribution, Mean variance, m.g.f, p.g.f and c.g.f. and its

applications, Exponential distribution, Gamma distribution, Beta

distribution of first and second kind, Mean variance, m.g.f, p.g.f and

c.g.f. and its applications

25

3. Properties and Applications of Standard Distributions: Normal

distribution as a limiting case of Binomial and Poisson distribution

(without proof). Additive properties of Bernoulli, Binomial, Poisson

and Normal distribution and its applications.

25

4. Sampling from Normal distribution: Sampling distributions of Mean

and variance, Chi-square, t, and F distributions and examples 25

Teaching-

Learning




Page 2 of 3

Methodology

Evaluation Pattern

Sr.

No.





15%



1. Have knowledge related to concept of discrete and continuous random variable and its

probability distributions including expectations and moments

2. Knowledge of important discrete and continuous probability distributions and their

interrelations, if any.


Sr.

No.

References

1. Gupta S.C. and Kapoor V.K. Fundamentals of Mathematical Statistics

2. Richard Johnson and Gouri Bhattacharya, Statistics-Principles and methods

3 Robert V. Hogg and Elliot Tanis : Introduction to Mathematical Statistics Fourth Edition


On-line Resources




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*****




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Title of the

Course FOUNDATION OF STATISTICS - II

Total Credits

of the Course 02

Hours per

Week 02

Course

Objectives:





3. To study an association between two attributes and various measures

4. To study normal distribution and its applications in various fields.

Course Content


(%)

1. Correlation and regression: Meaning, Types of correlation, Methods of

studying correlation, Scatter diagram(plot) method, Karl-Pearson’s

correlation coefficient method, Spearmen’s rank correlation coefficient

method, Properties of correlation coefficients ( without proof),

Examples,

Regression: Meaning, Properties of regression coefficients (without

proof), Examples

25

2. Association of Attributes: Theory of attributes, Consistency of data,

Independence and association of attributes, Measures of association

and contingency 25

3. Discrete probability distributions: Binomial and Poisson and its

applications 25

4. Continuous probability distribution: Normal distribution and its

applications 25




Page 2 of 3

Teaching-

Learning

Methodology

Evaluation Pattern

Sr.

No.





15%





3. differentiate between coefficient of correlation coefficients of association.

4 understand the applications of normal distribution in real life problems.


Sr.

No.

References

1. Gupta S.C. and Kapoor V.K. : Fundamentals of applied statistics

2. Gupta S.C.: Fundamentals of statistics

5




Page 3 of 3


On-line Resources

*****




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Title of the

Course OPERATIONS RESEARCH - II

Total Credits

of the Course 02

Hours per

Week 02

Course

Objectives:

1. Be able to identify the special features of assignment problem.

2. Be familiar with the types of problems that can be solved by applying

an assignment model.

3. Be familiar with basics of game theory

4. Be able to understand the basic concepts of network analysis.

Course Content


(%)

1. Assignment Problem: Introduction, Mathematical formulation of

Assignment problem, Hungarian Assignment method, Unbalanced

Assignment Problem, Maximal Assignment Problem 25

2. Elements of Game theory: Introduction, Two person zero sum game,

Games with saddle point: Maximin-Minimax principle, Strictly

determinable game, Fair Game 25

3. Game theory: Games without saddle point:, Solution of 22 game

(Without proof), Graphical method of solving m2 and 2n games,

Dominance property 25

4. Network analysis: Network scheduling, Introduction, Network & Basic

components, Rules of network construction, CPM Technique (Critical

path in Network Analysis), Float of an activity and even, Event Float,

Activity float, (i) Total float, (ii) Free float, (iii) Independent float,

Determination of the critical path, Determination of float

25

Teaching-




Page 2 of 3

Learning

Methodology

Evaluation Pattern

Sr.

No.





15%



1. understand the usage of game theory and network analysis.

2. understand the use of assignment problems

3. understand selected models and concepts of game theory

4 understand the concept and importance of network analysis.


Sr.

No.

References

1. Sharma S.D. : Operations Research

2. Sharma J.K. : Operations Research

3 Taha Hamdy A. : Operations Research





Page 3 of 3

On-line Resources

*****




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Title of the

Course BIOSTATISTICS - II

Total Credits

of the Course 02

Hours per

Week 02

Course

Objectives:





3. To learn the basic concepts in testing of hypotheses

4. To learn large and small sample test and its applications in biosciences or

medical sciences.

Course Content


(%)

1. Correlation and regression: Meaning, Types of correlation, Methods of

studying correlation, Scatter diagram(plot) method, Karl-Pearson’s

correlation coefficient method, Spearman’s rank correlation coefficient

method, Properties of correlation coefficients ( without proof),

Applications,

Regression: Meaning, Properties of regression coefficients (without

proof), Applications

25

2. Continuous Probability distribution: Normal distribution, Definition,

Properties (without proof), Area under normal curve, Applications 25

3. Test of Significance – I: Test of independence, Large sample test: test

for population proportion, test for difference between two population

proportions, test for population mean, test for difference between two

population means

25

4. Test of Significance – II: Small sample test: test for population mean,

test for difference between two population means (Unpaired t - test),

test for difference between two population means (Paired t - test) 25




Page 2 of 3

Teaching-

Learning

Methodology

Evaluation Pattern

Sr.

No.





15%





3. understand and use of normal distribution in real life.

4 use the concepts of testing of hypotheses, large and small sample test.


Sr.

No.

References

1. Gupta S.C. : Mathematical Statistics

2. Mahajan B.K. : Methods in Biostatistics

3 Sancheti D.C. and Kapoor V.K. : Statistics




Page 3 of 3

4 Wayne W. Daniel: Biostatistics - A foundation for analysis in the health sciences


On-line Resources

*****

SARDAR PATEL UNIVERSITY B.Sc. Statistics New CBCS

Semester - V (Effective From June 2020)

Sr. No. Subject Code Subject Name Credit 1 US05CSTA21 Mathematical Statistics 4 2 US05CSTA22 Theory of estimation 4 3 US05CSTA23 Survey sampling 4 4 US05CSTA24 Statistical quality control 4 5 US05CSTA25 Statistics Practicals 6 6 US05DSTA26 Statistical data analysis using software

packages 2

Total Credits 24

SARDAR PATEL UNIVERSITY Vallabh Vidyanagar, Gujarat


Page 1 of 3

(Bachelor of Science in Statistics) (Bachelor of Science) (B. Sc.) (Statistics) Semester (V)

Course Code US05CSTA51 Title of the

Course MATHEMATICAL STATISTICS

Total Credits of the Course 04 Hours per

Week 04

Course Objectives:

1. To understand the key concepts in probability and distribution theory 2. To understand the concepts of various inequalities, law of large

numbers 3. To learn various discrete probability distributions as a particular case of

power series distribution 4. Large sample results such as the central limit theorem will be used to

approximate a sampling distribution 5. To learn various continuous probability distributions 6. Emphasis is placed on theoretical understanding combined with

problem solving.

Course Content

Unit Description Weightage* (%)

1. Probability: Probability of union of 𝑛𝑛 events, Boole’s inequality, Bonferroni’s inequality, convergence in probability and in distribution, Chebychev’s inequality, Weak law of large numbers, Characteristic function and its properties (without proof)

25

2. General statement of Central Limit Theorem (CLT), Lindberg Levy form, Statement of Liapunov form (without proof). Applications of Central Limit Theorem (CLT).

25

3. Power Series Distributions:

Definition, p.g.f and m.g.f. of PSD, the recurrence relations between raw moments and central moments of PSD. The results of known discrete distributions as particular cases. Truncated Binomial and Truncated Poisson distributions (truncated at 𝑋𝑋 = 0)

25

4. Continuous Probability Distributions:

Lognormal, Cauchy, Laplace and Weibull distributions. Moments and their relations. Incomplete Gamma and incomplete Beta distributions

25



Page 2 of 3

as tail probabilities of Poisson and Binomial distributions. Truncated Normal distribution (Truncated at left)

Teaching-Learning Methodology

Evaluation Pattern

Sr. No.



2. Internal Continuous Assessment in the form of Practical, Viva-voce, Quizzes, Seminars, Assignments, Attendance (As per CBCS R.6.8.3)

15%



1. learn key concepts of probability and probability distributions

2. learn central limit theorem and its applications in understanding the concepts of statistical inference.


Sr. No.

References

1. Dudewic and Misra: Modern Mathematical Statistics, John Wiley & Sons.

2. Mukhopadhyay, P.(2006): Mathematical Statistics, 3ed., Books abd Allied(P) Ltd.

3 Rohatgi, V.K. & A.K. Md.E. Saleh (2001): An Introduction to Probability and Statistics, John Wiley (2nd Edition)

4 Gupta, S.C. and Kapoor, V.K.: Fundamentals of Mathematical Statistics, Sultan



Page 3 of 3

Chand and Sons

5 Hogg, Mckean and Craig : Introduction to Mathematical Statistics, 8th edition


On-line Resources

*****



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Course Code

US05CSTA52 Title of the

Course THEORY OF ESTIMATION

Total Credits of the Course

04 Hours per

Week 04

Course Objectives:

1. To learn the concepts of point estimation , methods including method of moments and maximum likelihood, bias and variance, mean squared error, sufficiency, completeness, the Cramer – Rao inequality, uniformly minimum variance unbiased estimators.

2. Confidence intervals construction methods, including likelihood based intervals, inversion methods, intervals based on pivots.

Course Content


1. Point Estimation – I

Estimation: Concepts of estimation, unbiasedness, consistency and efficiency. Rao – Cramer inequality, Fisher’s information, Minimum Variance Bound Unbiased Estimators (MVBUE).

25

2. Sufficiency: Fisher Neyman factorization criterion (theorem) (for one parameter discrete distributions with proof and for continuous distributions without proof).

25

3. Point Estimation – II

Methods of Estimation:

Methods of moments, method of maximum likelihood. Properties of maximum likelihood estimation (Without proof). Method of iteration for maximum likelihood estimators (Method of scoring)

25

4. Interval estimation:

Random interval, definition of confidence interval, confidence intervals for the parameters of a normal distribution, for difference of two normal means, for ratio of two normal variances, for binomial

25



Page 2 of 3

proportion and for difference of two binomial proportions.


Evaluation Pattern

Sr. No.




15%



1. explain in detail the notion of a parametric model and point estimation of the parameters of those models.

2. explain in detail and demonstrate approaches to include a measure of accuracy for estimation procedures and our confidence in them by examining the area of interval estimation.


Sr. No.

References

1. Hogg, R.V., Tanis, E.A. and Rao J.M. (2009): Probability and Statistical Inference, Seventh edition, Pearson Education, New Delhi



Page 3 of 3

2. Miller, Irwin and Miller, Marylees (2006): John E. Freund’s Mathematical Statistics with applications, (7th Edition), Pearson Education, Asia

3 Dudewic and Misra: Modern Mathematical Statistics, John Wiley & Sons.

4 Hogg, R.V. and Craig, A.T. (1972): Introduction to Mathematical Statistics, Amerind Publishing Co.

5 Lehmann, E.L. (1983): Theory of Point Estimation, Wiley Eastern

6 Robert V. Hogg and Elliot Tanis : Probability and Statistical Inference, 8th edition


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Course Code


Course SURVEY SAMPLING


04 Hours per

Week 04

Course Objectives:

1. To introduce the basic concepts of survey sampling theory including brief introduction to questionnaire design, methods of sample selection, estimation, sampling variance, standard error of estimation in finite population

2. Development of sampling theory for use in sample survey problems and sources of errors in surveys.

3. Practical examples will be used to illustrate the principles and methods.

Course Content


1. Basics of Survey sampling and Equal Probability Sampling Scheme:

Concept of population and sample, Complete enumeration V/S sampling. Basic principles of sample survey.

Simple Random Sampling (SRS) with and without replacement, definition and procedure of selecting a random sample, estimates of population mean, total and proportion, variances of these estimates, estimates of their variances.

25

2. Stratified Random Sampling: Technique, estimates of population mean and total, variances of these estimates, proportional and optimum allocations and their comparison with SRS. Practical difficulties in allocation.

25

3. Systematic sampling: Technique, estimates of population mean and total, variances of these estimates (𝑁𝑁 = 𝑛𝑛𝑛𝑛). Comparison of systematic sampling with SRS and stratified random sampling.

25



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4. Determination of sample size: Determination of sample size for proportion and continuous data in case of SRS. Cluster sampling (Equal clusters only) (Introduction only)

Sampling and non – sampling errors.

25


Evaluation Pattern

Sr. No.




15%



1. understand and interpret real life survey reports

2. understand concepts and techniques in sampling methods

3. understand solution methodology to estimate population parameters


Sr. No.

References

1 Cochran W.G. (1984): sampling Techniques (3rd Edition), Wiley Eastern



Page 3 of 3

2. Sukhatme, P.V., Sukhatme, B.V.: Sampling Theories of Survey With Application, IOWA State University Press and Indian Society of Agricultural Statistics

3 Murthy M.N. (1977): Sampling Theory & Statistical Methods, Statistical Pub. Society, Calcutta.

4 Gupta, S.C. And Kapoor, V.K. (2005): Fundamentals of Applied Statistics, Sultan Chand & Sons


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Course Code


Course STATISTICAL QUALITY CONTROL


04 Hours per

Week 04

Course Objectives:

1. To understand the concepts underlying statistical quality control 2. To develop ability to apply those concepts to the design and

management of quality control processes in industries 3. To apply statistical tools to analyze, design and use of various charts for

quality control

Course Content


1. Quality:

Definition, dimensions of quality, Quality system and standards. Introduction to ISO quality standards, Quality registration.

Statistical Process Control (SPC), chance and assignable causes of quality variation.

25

2. Statistical quality control charts:

Construction and statistical basis of 3𝜎𝜎 control charts.

Control charts for variable: X – bar & R chart, X – bar and S chart.

Control charts for attribute: 𝑝𝑝 – chart, 𝑛𝑛𝑝𝑝 chart, 𝐶𝐶 chart and 𝑢𝑢 chart. Comparison between control charts for variables and attributes.

25

3. Acceptance sampling plan:

Principles of acceptance sampling plans. Single sampling plan their OC, AQL, LTPD, AOQ, AOQL, ASN and ATI functions with graphical interpretations.

25

4. Double sampling plans their OC, AQL, LTPD, AOQ, AOQL, ASN and ATI functions.

25



Page 2 of 3


Evaluation Pattern

Sr. No.




15%



1. understand the basic concepts of quality, quality control and tools to improve quality

2. demonstrate the ability to use and interpret control charts for variables and attributes understand the concepts of various acceptance sampling plans

3. understand the concepts of various acceptance sampling plans


Sr. No.

References

1. Montogomery, D.C. (2009): Introduction to Statistical Quality Control, 6th Edition, Wiley India Pvt. Ltd.

2. Mukhopadhyay, P (2011): Applied Statistics, 2nd Edition revised reprint, Books and Allied (P) Ltd.



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3 Gupta, S.C. And Kapoor V.K.(2005): Fundamentals of Applied Statistics, Sultan Chand & Sons

4 Chapman and Hall, - Brownlee, K.A.(1960): Statistical Theory and Methodology in Science and Engineering, john Wiley & Sons.


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Course Code

US05DSTA56 Title of the

Course STATISTICAL DATA ANALYSIS USING SOFTWARE PACKAGES


02 Hours per

Week 02

Course Objectives:

1. To understand the basic concepts of loading data, plotting graph, generating different descriptive statistical measures, correlation and regression analysis using statistical softwares

2. To generate random numbers and understand the concepts of fitting of polynomials and exponential curves and normal probability plot using statistical softwares

3. To learn to do simple analysis and create and manage statistical analysis and understand the concepts of hypotheses testing.

Course Content


1. Learn how to load data, plot a graph viz. histograms (equal class intervals and unequal class intervals), Box – plot, Stem – leaf, frequency polygon, pie chart, ogives with graphical summaries of data.

25

2. Generate automated reports giving detailed descriptive statistics, correlation and regression.

25

3. Random number generation and sampling procedures. Fitting of polynomials and exponential curves. Application problems based on fitting of suitable distribution. Normal probability plot.

25

4. Simple analysis and create and manage statistical analysis projects, import data, code editing, Basics of statistical inference in order to understand hypotheses testing and compute p – values and confidence intervals.

25

Teaching-



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Learning Methodology

Evaluation Pattern

Sr. No.




15%



1. do graphical presentation, fitting of various curves and hypotheses testing based on given data and is able to do statistical analysis of the data.


Sr. No.

References

1. Moore, D.S. and McCabe, G.P. and Craig, B.A. (2014): Introduction to Practice of Statistics, W.H.Freeman.

2. Cunningham, B.J. (2012): Using SPSS: An Interactive Hands on approach.


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SARDAR PATEL UNIVERSITY B.Sc. Statistics New CBCS

Semester - VI (Effective from June – 2020)

Sr. No. Subject Code Subject Name Credit 1 US06CSTA21 Sampling distributions 4 2 US06CSTA22 Testing of hypothesis 4 3 US06CSTA23 Design of experiments 4 4 US06CSTA24 Operations Research 4 5 US06CSTA25 Statistics Practicals 6 6 US06DSTA26 Introduction to R programming 2

Total credits 24



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(Bachelor of Science in Statistics) (Bachelor of Science) (B. Sc.) (Statistics) Semester (VI)

Course Code


Course SAMPLING DISTRIBUTIONS


04 Hours per

Week 04

Course Objectives:

1. To understand the concepts of sampling distributions and their applications in statistical inference

2. To learn bivariate normal distribution and its applications 3. To learn the concepts of order statistics applicable in understanding the

concepts of non - parametric tests

Course Content


1. Sampling distributions:

Distribution of function of one and two random variables. Distribution function technique, change of variable techniques, m.g.f and characteristic function techniques.

25

2. Exact sampling distribution - I

Chi – square distribution: Definition and derivation of pdf of 𝜒𝜒2 with 𝑛𝑛 d.f. using m.g.f technique, nature of pdf curve for different degrees of freedom, mean, variance, m.g.f ,c.g.f., additive property and limiting form of 𝜒𝜒2 distribution.

25

3. Exact sampling distribution – II:

t – distribution: Student’s t and Fisher’s t – distribution, derivation of its pdf, nature of pdf curve with different degrees of freedom, mean, variance, moments and limiting form of t – distribution. F – distribution: Snedecor’s F – distribution, derivation of pdf, nature of curve with different degrees of freedom, mean, variance. Distribution of ratio of F – distribution.

25



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4. Bivariate Normal distribution:

Bivariate normal distribution as a particular case of multivariate normal distribution. Distribution of sample correlation coefficient 𝑟𝑟.

Order statistics: Definition: distribution of 𝑟𝑟𝑡𝑡ℎ order statistics. Joint pdf of 𝑟𝑟𝑡𝑡ℎand 𝑘𝑘𝑡𝑡ℎ order statistics. Distribution of sample range and sample median (for continuous distribution only)

25


Evaluation Pattern

Sr. No.




15%



1. derive probability distributions of functions of one and two variables using various techniques like m.g.f, distribution function and change of variable.

2. derive probability distributions of various sampling distributions like chi square, t and F distributions applicable in understanding the concept of testing of hypotheses


Sr. References



Page 3 of 3

No.


2. Gupta, S.C. and Kapoor, V.K.: Fundamentals of Mathematical Statistics, Sultan Chand and Sons

3 Mukhopadhyay, P.(2006): Mathematical Statistics, 3ed., Books abd Allied(P) Ltd.

4 Rohatgi, V.K. & A.K. Md.E. Saleh (2001): An Introduction to Probability and Statistics, John Wiley (2nd Edition)


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Course Code


Course TESTING OF HYPOTHESIS


04 Hours per

Week 04

Course Objectives:

Hypothesis testing methods, including likelihood ratio tests, the Neyman – Pearson lemma and uniformly most powerful tests, power calculations, Bayesian approaches and non – parametric approaches.

Course Content


1. Principles of Test of significance:

Null and alternative hypotheses (Simple and composite), Type – I and Type – II errors, critical region, level of significance, size and power, Best critical region, Most powerful (MP) test, Uniformly Most Powerful (UMP) Test, Neyman Pearson lemma (Statement and applications to construct most powerful test).

25

2. Likelihood Ratio (LR) test, Properties of LR test (without proof). Applications of LR test (𝑖𝑖) mean and variance of normal distribution (𝑖𝑖𝑖𝑖) equality of variances of two independent normal distributions

25

3. Sequential Analysis:

Sequential Probability Ratio Test (SPRT) for simple v/s simple hypotheses. Determination of stopping bounds 𝐵𝐵 and 𝐴𝐴. OC and ASN functions of SPRT.

25

4. Non - Parametric Tests:

One sample and two sample sign test. Wald – Wolfwitz run test, Run test for randomness, Median test, Wilcoxon – Mann – Whitney test.

25



Page 2 of 3


Evaluation Pattern

Sr. No.




15%



1. demonstrate the plausibility of pre – specified ideas about the parameters of the models by examining the area of hypothesis testing

2. explain in detail and demonstrate the use of non – parametric statistical methods.


Sr. No.

References

1. Ross, S.M.: Introduction to Probability and Statistics for Engineers and Scientists, Elsevier


3 Hogg, R.V. and Craig, A.T. (1972): Introduction to Mathematical Statistics, Amerind Publishing Co.

4 Gupta, S.C. and Kapoor, V.K.: Fundamentals of Mathematical Statistics, Sultan



Page 3 of 3

Chand and Sons

5 Robert V. Hogg and Elliot Tanis : Probability and Statistical Inference, 8th edition


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Course Code


Course DESIGN OF EXPERIMENTS


04 Hours per

Week 04

Course Objectives:

1. To learn how to plan, design and conduct experiments efficiently and effectively and analyze the data to obtain objective conclusions

2. Understanding the process of designing an experiments

Course Content


1. One Way Analysis of Variance and Completely Randomized Design (CRD)

For fixed effect model one way classification – Purpose and Analysis with equal number of observations per cell using ANOVA technique.

Concept of treatment, plot, block, yield, shapes and sizes of plots and blocks. Principles of experimental design: Randomization, Replication and Local Control.

Complete Randomized Design (CRD) – Introduction, Layout, Statistical analysis and its merits and demerits.

25

2. Two way Analysis of Variance and Randomized Block Design (RBD)

Two way classification – Purpose and Analysis with equal number of observations per cell using ANOVA technique – Expected values of sum of squares for both one way and two way classifications.

Randomized Block Design (RBD) – Introduction, layout, Statistical analysis and its merits and demerits.

Estimation of one and two missing yields. Efficiency of RBD over CRD.

25

3. Latin Square Design (LSD) : Introduction, layout, Statistical analysis and its merits and demerits. 25



Page 2 of 3

Estimation of one and two missing yields. Efficiency of LSD over RBD and CRD.

4. Factorial Experiments: Factorial experiments upto four factors each at two levels. Concept of confounding and their types. Confounding upto two interactions. Analysis of confounded factorial experiments.

25


Evaluation Pattern

Sr. No.




15%



1. appreciate the advantages and disadvantages of a design for a particular experiment

2. construct optimal or good designs for a range of practical experiments

3. understanding the potential practical problems in its implementation describe how the analysis of the data from the experiment should be carried out.


Sr. No.

References



Page 3 of 3

1. Das, M.N. & Giri, N.: Design of experiments (Wiley Eastern Ltd)

2. Montogomery D.C. (1976): Design and Analysis of Experiments, John Wiley

3 Cochran W.G. & Cox G.M.: Experimental Designs, John Wiley

4 Mukhopadhyay P. (1999): Applied Statistics

5 Federer W.T. (1975): Experimental Designs – Theory and Application, Oxford & IBH.


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Course Code


Course OPERATIONS RESEARCH


04 Hours per

Week 04

Course Objectives:

1. To impart knowledge in concepts and tools of Operations Research 2. To formulate verbal problem into mathematical form 3. To understand mathematical tools that are needed to solve optimization

problems used in Operations Research 4. To apply techniques constructively to make effective business

decisions.

Course Content


1. Linear Programming Problem (LPP), Mathematical formulation of LPP, Graphical solutions of a LPP. Simplex method for solving LPP. Special cases of LPP. Concept of duality in LPP, Dual simplex method.

25

2. Transportation Problem (TP): Initial solution by North – West corner rule, Least cost method and Vogel’s approximation method (VAM), Modi’s method to find the optimum solution, special cases of transportation problem.

Assignment Problem: Hungarian method to find optimal assignment, special cases of assignment problem.

25

3. Game Theory: Rectangular game, minimax – maximin principle, solutions to rectangular game using graphical method, dominance property to reduce the game matrix and solution to rectangular game with mixed strategy.

25

4. PERT and CPM: Project planning with PERT and CPM: Drawing of Project network, critical path identification, slack time and float. Calculation of probability of completing project within a specified

25



Page 2 of 3

time.


Evaluation Pattern

Sr. No.




15%



1. solve Linear Programming problems

2. solve Transportation and Assignment Problems

3. understand the usage of game theory and network analysis.


Sr. No.

References

1. KantiSwarup, Gupta R.K. and Manmohan (2007): Operations Research, 13th Edition, Sultan Chand and Sons.

2. Taha, H.A. (2007): Operations Research: An Introduction, Prentice Hall of India.



Page 3 of 3

3 Heardly, G. (1962): Linear Programming


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((Bachelor of Science in Statistics) (Bachelor of Science) (B. Sc.) (Statistics) Semester (VI)

Course Code

US06DSTA56 Title of the

Course INTRODUCTION TO R

PROGRAMMING Total Credits of the Course

02 Hours per

Week 02

Course Objectives:

This course introduces the statistical computing language R (open source and free software) for under graduate students with no prior background in R or programming.

Course Content


1. Introduction to R: R as a Statistical Software and language, R preliminaries, methods of data input, Data accessing or indexing, Data frames and lists, Functions, Graphics with R, Saving, storing and retrieving work, work space and files, using scripts, using packages.

Descriptive Statistics Using R: Diagrammatic and graphical representation of data, Measures of central tendency, dispersion, skewness and kurtosis, selection of representative samples.

25

2. Probability and Probability distributions using R:

Probability : definition and properties, probability distributions, some special discrete distributions (Binomial, Poisson), Continuous probability distributions, some special distributions(Normal, Exponential)

Methods for generating random variables: Introduction, Random generation of common probability distribution in R, the inverse method, the acceptance and rejection methods, transformation methods

25

3. Correlation and Regression analysis: Correlation, correlation coefficient, Linear Regression, inference procedure for simple linear model, validation of linear regression model. Monte Carlo estimation and standard error. Estimation of MSE, estimating a confidence interval, Monte Carlo methods for hypothesis test, Empirical type – I

25



Page 2 of 3

error, Power of a test, Comparison of powers of two tests

4. Statistical Inference: Sampling distribution of the sample mean, Estimation of parameters, plots to check normality, Hypothesis testing, Goodness of fit, One way and Two way ANOVA

25


Evaluation Pattern

Sr. No.




15%



1. understand the basic concepts such as data type and index and use them in their work

2. demonstrate the use of basic functions

3. create their own customized functions

4 construct tables and graphs for descriptive statistics

5 import, review, manipulate and summarize data sets in R

6 explore data sets to create testable hypotheses and identify appropriate statistical tests

7 perform appropriate statistical test using R



Page 3 of 3

8 create and edit visualization with R.


Sr. No.

References

1. Chambers J.M. (1998) : Programming with Data: A guide to S language, Springer

2. Statistics Using R – Purohit, S.G., et al. (2008), Narosa Publishing House

3 Statistical Computing with R – Rizzo, M.L. (2007), Chapman & Hall / CRC


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Documents

Programme Learning Outcomes in B.Sc. Statistics 1. 2. 3. 4....SARDAR PATEL UNIVERSITY B.SC. SYLLABUS STATISTICS SEMESTER – III Effective from June, 2019 Sr. No. Course code Title