Evaluation Scheme andSyllabus

B.Sc.

Department of StatisticsFaculty of Science

Maharishi University of Information TechnologyLucknow

MAHARSHI UNIVERSITY OF INFORMATION TECHNOLOGY LUCKNOW

COURSE NAME :B.Sc. (Statistics) – I Year Semester - I Semester COURSE CODE :

DURATION OF COURSE : 3 years

Sr No. Code

SUBJECT PERIODSEVALUATION SCHEME

Credits

THEORY SESSIONSAL EXAM

TotalL TU P AETA

CT Total

1 BST101 Probability Theory I 3 0 - 10 20 30 70 100 4

2 BST102 Descriptive Statistics I 3 0 - 10 20 30 70 100 4

3 BST103 Viva -voce 3 0 - - - - - 100 4Total 12

B.Sc. (Statistics)- I SemPaper I: Probability Theory - I

UNIT – I Important Concepts in probability, Definition of Probability, Clasical and relative frequency approach to Probability, Random Experiment, Sample space, definition of an event and Exhaustive events. UNIT – II Conditional Probability, Independence of events, Baye’s Theorem, Proof of Baye’s Theorem, Bernoulli Trials, Generalization of Bernoulli’s Trials, Generalization of Bernoulli’s Trials. UNIT – III Random variable, Definition of discrete random variables, Probability mass function, Idea of continuous random variable, Probability density function, Illustrations of random variables and its properties. UNIT-IV Moments, Measures of location, Dispersion, Skewness and Kurtosis, Probability generating function (If it is existing), Moment generating function, their properties and uses. REFERENCE 1. Hogg & Craig: Mathematical Statistics. 2. Mood, Graybill and Boes: Introduction to the theory of Statistics.

Paper II: Descriptive Statistics - I

UNIT – IData, Types of data, Representation of data, concepts of a statistical population and Sample from a population, Qualitative and Quantitative data , Nominal and ordinal data, cross sectional and time series data, Discrete and continuous data, Frequency and Non frequency data.

UNIT-IIControlled experiment, sample surveys and Population Census, Method of conducting Population census with special reference to census in India, Analysis of categorical data. UNIT-IIIConstruction of tables with one or more factors of classification, classification on Geographical, Qualitative and quantitive diagrammatic representation of data , construction of sample , Bar diagram , Multiple bar diagram construction.

UNIT-IVFormation of frequency distribution, Relative frequency, Frequency density and cumulative frequency, Contraction of tables and frequency distribution using MS-Excel.

REFERENCES1. Cochran, W.G.: Sampling Techniques1. Sukhatme, Sukhatme, Sukhatme&Asok: Sampling Theory of Surveys with applications.

MAHARSHI UNIVERSITY OF INFORMATION TECHNOLOGY LUCKNOW

COURSE NAME :B.Sc. (Statistics) – I Year II - Semester

COURSE CODE :

DURATION OF COURSE : 3 years

Sr.No. Cod

e

SUBJECT PERIODSEVALUATION SCHEME

Credits

THEORY SESSIONSAL EXAM

TotalL TU P AETA

CT Total

1 BST201

Probability Theory-II3 0 - 10 20 30 70 100 4

2 BST202

Descriptive Statistics II3 0 - 10 20 30 70 100 4

3 BST 203

Viva -voce3 0 - - - - - 100 4

Total 12

B.Sc. (Statistics)-II SemPaper I: Probability Theory – II

UNIT – I Continuous Probability Distribution , Introduction, Normal Distribution, Gaussian distribution, Definition, Properties of Normal Distribution, Mean of Normal distribution.UNIT – IIRectangular or Uniform Distribution, Mean of Rectangular distribution, Standard deviation, Distribution Function of Rectangular distribution,UNIT – IIIExponential distribution, Distribution, Function of Exponential Distribution, Memoryless property of Exponential Distribution, Rayleigh Distribution.

UNIT-IVPoisson Distribution Function, Properties of Poissondistribution, Gamma, Beta distribution function.REFERENCE1. Hogg &Craig: Mathematical Statistics.2. Mood, Graybill and Boes: Introduction to the theory of Statistics.3. Goon, Gupta and Dasgupta: Fundamentals of Statistics Vol.1 & II

Paper II: Descriptive Statistics - II

UNIT – IMeaning and Definition of Statistics, Parametric test, Hypothesis Testing, Definition of statistics, Scope and Limitation of Statistics.UNIT-IIIndian Statistics , Evolution of Statistical system in India, Central Statistical Organization, Nature and scope of Economic statistics in India, Industrial statistics, National Sample Survey.UNIT-IIIMeasurement of Central tendency,Mean, Median, Mode, properties of central tendency, Merits and demerits of Central tendency. UNIT-IVStatistical Enquires, Scope of the problem, Method to be Employed, Other types of Enquires, Editing data.REFERENCES1. Cochran, W.G.: Sampling Techniques1. Sukhatme, Sukhatme, Sukhatme&Asok: Sampling Theory of Surveys with applications.2. Murthy, M. N.: Sampling theory.

MAHARSHI UNIVERSITY OF INFORMATION TECHNOLOGY LUCKNOW

COURSE NAME: B.Sc. (Statistics) – II Year III Semester

COURSE CODE :

DURATION OF COURSE : 3 years

Sr. No. Cod

e

SUBJECT PERIODSEVALUATION SCHEME

Credits

THEORY SESSIONSAL EXAM

TotalL TU P AETA

CT Total

1 BST301

Statistical Inference-I3 0 - 10 20 30 70 100 4

2 BST302

Sampling Survey-I3 0 - 10 20 30 70 100 4

3 BST303

Viva -voce3 0 - - - - - 100 4

Total 12

Paper I:Statistical Inference - I

UNIT – IPoint estimation-: Introduction, Population and sample, finite and Infinite Population, Real and hypothetical Populaton, Parameter and statistics, Theoretical Population and its Random Sample, sampling Distribution.

UNIT – IIEstimation, Type of Estimation, point estimate, Unbiased estimator, Consistent estimater, The method of Maximum Likehood, The Methid of Moments.

UNIT – IIITesting of Hypothesis- Introduction, Statistical and Parametric Hypothesis, Simple and composite Hypothesis, Null and Alternative Hypothesis

UNIT-IVCritical and acceptance Hypothesis, Two type of error, Level of significance, Power Function and power of a Test, P- value Test.

REFERENCE1. Hogg &Craig : Mathematical Statistics.2. Mood, Graybill and Boes : Introduction to the theory of Statistics.3. Goon, Gupta and Dasgupta : Fundamentals of Statistics Vol.1 & II

Paper II: Survey Sampling - I

UNIT – IIntroduction and Basic Concepts of Sampling, advantages of sample survey, Disadvantages of Sample Survey, Objective of the survey, Population to be sample, data to be collected Method of measurement, Selection of the sample. UNIT-IIConcepts, Definition and Termology, population, sample, Sampling Fraction, Sampling Unite Sampling Frame/ Sampling List, population parameter, Estimator.UNIT-IIICharacteristics of Interest, Selection of a sample, Sample space, Sampling Design, Sampling Error, Non- Sampling Error, sampling Distribution, Various Sampling procedures.UNIT-IVStratified Random sampling, Introduction, Advantages of stratified Random sampling over simple Random Sampling, Systematic sampling, Advantages of systematic sampling, Use of Systematic sampling.REFERENCES1. Cochran, W.G.: Sampling Techniques1. Sukhatme, Sukhatme, Sukhatme&Asok: Sampling Theory of Surveys with applications.2. Murthy, M. N.: Sampling theory.

MAHARSHI UNIVERSITY OF INFORMATION TECHNOLOGY LUCKNOW

COURSE NAME: B.Sc. (Statistics) – II Year IV Semester

COURSE CODE :

DURATION OF COURSE : 3 years

Sr.No. Code

SUBJECT PERIODSEVALUATION SCHEME

Credits

THEORY SESSIONSAL EXAM

TotalL TU P AETA CT Total

1 BST401

Statistical Inference-II4 0 - 10 20 30 70 100 4

2 BST402

Survey Sampling - II4 0 - 10 20 30 70 100 4

3 BST403

Viva -voce4 0 - - - - - 100 4

Total 12

B.Sc. (Statistics)- IV Sem

Paper I: Statistical Inference - II

UNIT – ITests of Significance, Introduction, Tests of significance for Attributes, Tests of significance for Difference in Proportions, Test of Significance in Case of Variables.

UNIT – IITests of Significance Based on x2 Distribution , Test of Significance Based on t- Distribution, Tests of significance Based on F- Distribution.UNIT – IIILikelihood Ratio Test , Properties of likelihood ratio test, Reduction of L.R Tests to standard Test, Test for the mean of a Normal Population.

UNIT-IVInterval Estimation, Pivotal method or Central Method , Central Confidence Interval, one sided confidence limits , Length of a condidence Interval.REFERENCE1. Hogg &Craig : Mathematical Statistics.2. Mood, Graybill and Boes : Introduction to the theory of Statistics.3. Goon, Gupta and Dasgupta : Fundamentals of Statistics Vol.1 & II

Paper II: Survey Sampling - II

UNIT – IRatio and Regression Method of Estimation, Introduction, Concept of R and R, Notations and Terminology, Ratio Estimator, Bias of the Ratio Estimator.UNIT-IISome other sampling schemes, cluster sampling , Advantages of cluster sampling , Disadvantages of cluster sampling, Notations and Terminology, Difference between stratified Random Sampling and cluster sampling.UNIT-IIIDouble sampling in Ratio Method of Estimation, Method of Estimation ,Regression Estimate in Double sampling, Mean square Error of Regression Estimate.UNIT-IVNon-sampling and sampling Errors, Introduction , Classification of Errors , Types of Non – Sampling Errors, Control Measure.REFERENCES1. Cochran, W.G.: Sampling Techniques1. Sukhatme, Sukhatme, Sukhatme&Asok: Sampling Theory of Surveys with applications.2. Murthy, M. N. : Sampling theory.

MAHARSHI UNIVERSITY OF INFORMATION TECHNOLOGY LUCKNOW

COURSE NAME B.Sc. (Statistics) – III Year V- Semester

COURSE CODE :

DURATION OF COURSE : 3 years

Sr.No. Cod

e

SUBJECT PERIODSEVALUATION SCHEME

Credits

THEORY SESSIONSAL EXAM

TotalL TU P AETA

CT Total

1 BST501

Applied Statistics I

4 0 - 10 20 30 70 100 42 BST

502Numerical Methods and Fundamentals of Computers

4 0 - 10 20 30 70 100 43 BSP

5o3Viva -voce

4 0 - 100 4

Total 12

B.Sc. Semester-V

Paper-I Applied Statistics I

UNIT-I (Index Number: Definition, problems involved in the construction of index numbers,calculation of index numbers-simple aggregate method, weighted aggregates method,

UNIT-IITime series Analysis: Definition, components of time series-trend, seasonalvariations, cyclic variations, irregular component, illustrations, additive andmultiplicative models, determination of trend-graphic method, semi-averages method,method of curve fitting by principle of least squares, growth curves and their fitting.UNIT-III hospital records, measurement of mortality, crude death rate, specific death rate,standardized death rates, complete life tables and its main features, assumptions,descriptions and construction of life tables, uses of life tables,

UNIT-IVmeasurement of fertility-crude birth rate, general fertility rate, specificfertility rate, total fertility rate, measurement of population growth, gross reproductionrate, net reproduction Demographic methods: sources of demographic data-census, resigter, adhoc survey,rate.Books recommendedSr.No. Title of Book Name of author Publisher1. Applied General Croxton F.E., Cowden Prentice HallStatistics D.J. &Kelin S.

2. Demography Cox P.R. Cambridge Uni.Press3. Technical Ramakumar R. New AgeDemography International4. Fundamentals of Gupta S.C. & Sultan ChandApplied Statistics Kapoor V.K. & Son.

Paper-II- Numerical Methods and Fundamentals of Computers

UNIT-I Numerical Methods: Concept of intrapolation and extrapolation, difference tables,methods of interpolation, Newton’s formula for forward and backward interpolationwith equal intervals, Lagrange’s method of interpolation, Divided differences,Trapezoidal rule, Simpson’s 1/3rd and 3/8th formula.UNIT-II Basic of Computer: Introduction, origin, development, uses and limitation ofcomputers. Types of computers, computer structure, input-unit, CPU, output unit,secondary storage, High Level and low level languages, compiler and interpreter.UNIT-III Flow charts and Algorithm: Concepts of flow chart, algorithm and programming. Flowcharts and algorithms for the following: Mean, Standard Deviation,

UNIT-IVCoefficient ofCorrelation, Straight line fitting. Trapezoidal rule, Simpson’s 1/3 and 3/8 t h rules.

Books recommended

Sr.No. Title of Book Name of author Publisher1. Computer Sinha P.K. BPB PublicationFundamentals2. Introductory Sastry S.S. Prentice HallMethods ofNumericalAnalysis

MAHARSHI UNIVERSITY OF INFORMATION TECHNOLOGY LUCKNOW

COURSE NAME B.Sc. (Statistics) – III Year VI -Semester

COURSE CODE :

DURATION OF COURSE : 3 years

Sr.No. Cod

e

SUBJECT PERIODSEVALUATION SCHEME

Credits

THEORY SESSIONSAL EXAM

TotalL TU P AETA

CT Total

1 BST Statistical Quality 4 0 - 10 20 30 70 100 4

601 Control

2 BST602

Operations Research 4 0 - 10 20 30 70 100 4

3 BSP 603

Viva -voce4 0 - - - - - 100 4

Total 12

B.Sc. Semester-VIPaper-I - Statistical Quality Control

UNIT - I Statistical Quality Control: Meaning and uses of SQC, causes of variations inquality, product and process control, control charts, 3- control limits, control chartfor variables- X and R chart, criteria for detection of lack of control in X & R Charts,Interpretation of X & R charts, control chart for standard deviation (charts), c.UNIT-II Acceptance sampling: Problem of lot acceptance, stipulation of good and bad lots,producer’s and consumer’s risks, single and double sampling plans, their OC functions,

concepts of AQL, LTPD, AOQL, average amount of inspection and ASN function.UNIT-III Demand Analysis: Laws of demand and supply, price elasticity of demand, demandfunction with constant price elasticity, partial elasticties of demands (income elasticity& cross elasticity), types of data required for estimating elasticities, family budget.UNIT-IVData, time series data, Leontief’s and Pigous’s methods (from time series data) toestimate demand functions. Engel’s law, Pareto’s Law of income distribution, curvesof concentration, Lorenz curve and Gini’s coefficient

Books recommendedSr.No. Title of Book Name of author Publisher1. Statistical Quality Grant E.L. McGraw HillControl2. Statistical Methods Cowden D.J. Asia Pub.in Quality Control Society.

B.Sc. Semester-VI

Paper-II- Operations Research

UNIT-I Objective of O.R., nature and definitions of O.R., Scope of O.R., Meaning andnecessity of O.R. models, classification of O.R. models, Advantages & disadvantagesof O.R. models. Steps in model formulation, principles of modeling. Characteristics ofa good model, Allocation problems, General linear programming problem, formulationof G.L.P.P., (formulation only for Transportation problem, trim loss problem, productmix problem, Diet problem).UNIT-II Linear programming problem; definition, objective function, constraints, graphicalsolution of L.P.P., limitations of graphical method, simplex method to solve L.P.P.

UNIT-III Transportation Problem(T.P.), Formulation of T.P., B.F.S. of T.P., Different methodsto find initial feasible solution, North-West corner rule, Row minima method, columnminima method,

UNIT-IVMatrix minima method (Least cost entry method), Vogel’sApproximation method (or Unit cost penalty method). UV-method (Modi-method) forfinding the optimum solution of T.P

Books recommendedSr.No. Title of Book Name of author Publisher1. Operations Hillier F.S. & Tata McGrawResearch Lieberman G.J. Hill2. Linear Hadley G. NarosaProgramming