POKHARA UNIVERSITY

Level: Bachelor Semester – Spring Year : 2010Programme: BE Full Marks: 100Course: Probability and Statistics Pass Marks: 45

Time : 3hrs.

Candidates are required to give their answers in their own words as far as practicable.The figures in the margin indicate full marks.Attempt all the questions.

1. a) The marks obtained by 50 students in numerical methods are given as:

65 36 49 84 79 56 28 43 67 3643 78 37 40 68 72 70 55 62 8288 50 60 56 57 46 39 57 22 6559 48 76 74 80 69 51 40 56 4535 21 62 52 63 32 86 64 53 34

i. Construct a frequency distribution from the above data. What additional information did your receive from frequency distribution that you didn't receive from the original raw data? Also mention the steps of constructing a frequency distribution.

ii. Represent the data by means of cumulative frequency curve.iii. Identify the median and first quartile from the curve.

b) Following information are obtained about two batsman of a cricket team.

Player A Player BNo. of Matches 35 40Average Runs 65 70Standard Deviation 10 15

Find the combined mean & standard deviation of runs of two players. Which player is more consistent and why? What would be the effect of combined mean if both player A and B play equal number of matches?

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2. a) Three machines A, B and C produce respectively 50%, 30% and 20% of the total number of items of a factory. The percentages of defective output of these machines are 3%, 4%, and 5% respectively.

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If an item is selected at random, find:i. the probability of defective item

ii. the probability that the defective item is produced by machine A, produced by machine B and produced by machine C.

b) Prove that: P(B/A) =

Where P(B/A) is conditional probability of B when A has already happened.

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3. a) A probability density function is given as:

F(x) = ; 0x2

= 0 Otherwise. Find i) P(x>0)

ii) F(1.5)iii) P(0<x1)

b) Joint distribution of x and y are given by:

f(x,y) = 4xye ; x0, y 0

i. test whether x and y are independentii. find the conditional density of x given y = y.

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4. a) In a particular College in Nepal it has been found that 20% of the students withdraw without completing the Engineering course, assume that 15 students have register in a new semester what is the probability that:

i. none will withdraw the courseii. at most two will withdraw the course

iii. find the mean of this distribution.b) The average number of network errors experienced in two hours

period is 6 What is the probability that in any given hour:i. exactly two network errors will occur

ii. at least two network error will occur

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c) Incomes of a group of 1000 persons were found to be normally distributed with mean Rs. 520 and standard deviation Rs. 60 Find the number of persons whose income lies between Rs. 460 to Rs. 640.

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5. a) A machine put out 16 defective articles in a sample of 600 articles. After machine is overhaulted, it puts out 1 defective articles in sample of 100 articles. Has the machine improved? Suggest your answer at 5% level of significance?

b) The average height of 50 students who showed no athletic interest was 68.2 inches with standared deviation of 2.5 inches, while another set of 50 students who showed athletic interest was average height of 67.5 inches with a standared deviation of 2.8 inches. Test the hypothesis that the atheletics makes student taller.

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6. a) The manufacturer of Shilpa elecric bulbs claims that mean life of their bulb is 25 months. A random sample of 9 such bulbs gave the following values: Life in months:24, 26, 32, 28, 20, 20, 23, 27 and 34Can you regard the manufacturer's claim to be valid at 5 percent level of significance?

b) Find the value of co-efficient of determination between x and y for the given data and interpret the result. Find also regression equation of Y on X. Test whether there is any significant relationship between X and Y at α = 0.05.

X: 1 2 3 4 5 6 7 8 9 10Y 10 12 16 28 25 36 41 49 40 50

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7. Write short notes on: a) The central limit theoremb) Approaches to probabilityc) Negative exponential distributiond) Measures of central tendenciese) Paired t-test

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