Download JNTUH MCA 1st Sem R17 2018 June-July 841AD Probability And Statistics Question Paper

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Code No: 841AD R17

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

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MCA I Semester Examinations, June/July - 2018

PROBABILITY AND STATISTICS

Time: 3hrs Max.Marks:75

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

Part A is compulsory which carries 25 marks. Answer all questions in Part A. Part B consists of 5 Units. Answer any one full question from each unit. Each question carries 10 marks and may have a, b, c as sub questions.

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PART - A 5 x 5 Marks = 25

1. A bag contains 26 red balls and 24 green balls. If one ball is randomly selected from this bag, find the probability that this ball is 1) red and 1ii) green. [5]
2. Define discrete and continuous random variables with an example of each. [5]
3. If a random sample of size 81 is taken whose variance is 20.25 and mean is 32, construct 98% confidence interval. [5]
4. Explain errors in sampling. [5]

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5. Derive normal equations to fit a straight line of the form y=ax+b for a given set of N data points (x_i,y_i),i=1,2, ..... N . [5]

PART -B 5 x 10 Marks =50

6. State and prove addition theorem of probability.

   Let A and B be two events with P(A n B) = 1/6, P(A n B) = 1/4 and P(B) = 1/3. Find i) P(A) ii) P(B) iii) P(A ? B). [5+5]

   OR

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   State and prove Baye’s theorem.

   A business man goes to hotels A, B, C, 20%, 50%, 30% of the times respectively. It is known that 5%, 4%, 8% of the rooms in A, B, C hotels have faulty plumbings. What is the probability that the business man’s room having faulty plumbing is assigned to hotel C? [5+5]

7. A random variable X has the following probability distribution.

   X : 0 1 2 3 4

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   P(X): C 2C 2C 3C C²

   Find 1) C and ii) the distribution function of X .

   A continuous random variable X has pdf f(x)= a(x² + 1) ,0<x<1.Find 1) ‘a’suchthat P(X <a)=P(X >a) and ii) mean of X [5+5]

   OR

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8. Find the mean and variance of Normal distribution. [10]

9. Let S = {1,5,6,8}. Find the probability distribution of the sample mean for random sample of size 2 without replacement. [10]

   OR

   In how many ways estimation can be done and what are they? Explain in detail. [10]

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10. In two large populations, there are 30% and 25% respectively of fair haired people. Is this difference likely to be hidden in samples of 1200 and 900 respectively from the two populations? [10]

    OR

    Two independent samples of sizes 8 and 7 had the following values.

    Sample A 11 11 13 11 15 9 12 14

    Sample B 9 11 10 13 9 8 10 -

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    Is the difference between the means of samples significant? [10]

11. Construct the least squares linear and quadratic approximations to the following data: [10]

    X : 1 2 3 4 5

    y : 2.1 2.5 3.7 5.0 4.2

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    OR

    Show that r = (s²_x + s²_y - s²_x-y) / (2s_xs_y) where s²_x, s²_y, s²_x-y are variances of x,y,x—y respectively. Hence find the correlation coefficient r for the following data: [10]

    X : 6 5 8 8 7 6 10 4 9 7

    y : 8 7 7 10 5 8 10 6 8 6

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