Download JNTUH MCA 1st Sem R13 2019 April-May 811AD Probability And Statistics Question Paper

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Code No: 811AD

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

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MCA I Semester Examinations, April/May - 2019

PROBABILITY AND STATISTICS

Time: 3hrs Max.Marks:60

Note: This question paper contains two parts A and B.

Part A is compulsory which carries 20 marks. Answer all questions in Part A. Part B consists of 5 Units. Answer any one full question from each unit. Each question carries 8 marks and may have a, b, c as sub questions.

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PART - A

5 x 4 Marks = 20

1. a) State and prove Baye’s theorem. [4]
2. b) A continuous random variable X has the distribution function
   0, x<1
   F(x)=1k(x—1*), 1<x<3
   

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   1 , x>3
   Determine i) p.d.f. and ii)k. [4]
3. c) If a population of size N = 35 and if all possible samples of size 2 are drawn from this population, find the finite population correction factor. [4]
4. d) Define type I and type II errors. [4]
5. e) Find the rank correlation coefficient for the following data: [4]
   

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   X	1	2	3	4
   y	5	4	3	2

PART - B

5 x 8 Marks = 40

1. A class consists of 6 girls and 10 boys. If a committee of 3 is chosen at random from the class, find the probability that
   a) 3 boys are selected b) exactly two boys are selected
   c) at least one boy is selected and d) exactly two girls are selected. [8]
   

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   OR
   State and prove addition theorem of probability. Three students A, B, C are in running race. If A and B have the same probability of winning and each is twice as likely to win as C, find the probability that B or C wins. [8]
2. a) If X is a continuous random variable, prove that
   i) E (a X+ b) = a E(X)+ b and ii) Var(a X+b )=a² Var (X).
   b) The probability density function of a continuous random variable X is
   

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   f(x)=9x², 1<x<8
   0 , otherwise
   Find the distribution function F(x). [4+4]
   OR
   a) If a Poisson distribution is such that P(X = 1) = P(X = 3) , find
   

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   i) the mean ii) P(X >1) iii) P(2< X <5).
   b) Find the moment generating function of the Poisson distribution. [5+3]
3. FirstRanker.com
   A population consists of five numbers 6, 8, 10, 12, 14. If all samples of size 2 are drawn from this population with replacement. Find
   a) the total number of samples with replacement.
   

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   b) the mean and standard deviation of the population and
   c) the mean and standard deviation of the sampling distribution of means. [8]
   OR
   Obtain an unbiased estimator of µ for a normal distribution with mean µ and variance s².
   Explain Bayesian estimation. [4+4]

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4. The length of life of certain computers is approximately normally distributed with mean 800 hours and standard deviation 40 hours. If a random sample of 30 computers has an average life of 788 hours, test the null hypothesis µ=800 hours against the alternative that µ?800 hours at
   a) 4% and b) 5% level of significance. [8]
   OR
   The students of two schools were measured for their heights. One school was in the east coast and another was in the west coast where there is a slight difference in weather. The sampling results are as follows.
   EastCoast: 43 45 48 49 51 51
   

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   WestCoast: 47 49 51 53 54 55 55 56 57
   Find whether there is any impact of weather on height, taking other variables as constant. Test at 5% level of significance. [8]
5. Using the method of least squares, fit a straight line and a second degree parabola to the following data: [8]
   

   X:	0	1	2	3	4
   y:	0	1.8	1.3	2.5	6.3

   
   OR
   

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   Find the correlation coefficient for the following bivariate frequency distribution. [8]
   

   X	21-25	26-30	31-35	36-40	41-45
   21-25	1
   26-30	3	1
   31-35	2	5	2
   36-40	1	4	1
   41-45		1	3
   46-50			1

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