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Posted By: Nitin Bajaj - Editor Member Level: Diamond Posted Date: 06 Mar 2008
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2007 Jawaharlal Nehru Technological University B.Tech November 2007 PROBABILITY AND STATISTICS - Set no 1 Question paper
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II B.Tech I Semester Regular Examinations, November 2007 PROBABILITY AND STATISTICS ( Common to Computer Science & Engineering, Information Technology and Computer Science & Systems Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks
1. (a) If A and B are events with P(A) = 1/3, P(B) = 1/4, and P(A U B) = 1/2, ?nd i. P(A/B) ii. P(A nB c ) (b) Three students A,B,C are in a running race. A and B have the same probability of wining and each is twice as likely to win as C. Find the probability that B or C wins. (c) The students in a class are selected at random one after the other for an examination. Find the probability that the boys and girls are alternate if there are i. 5 boys and 4 girls ii. 4 boys and 4 girls. [6+5+5]
2. (a) If X is a continuous random variable and K is a constant then prove that i. Var (X+K) = Var (X) ii. Var(kX) = k 2 Var (X) (b) Determine the probability of getting 9 exactly twice in 3 throws with a pair of fair dice. [8+8]
3. (a) The average number of phone calls/minute coming into a switch board between 2 p.m. and 4. p.m. is 2.5. Determine the probability that during one particular minute there will be i. 4 or fewer ii. more than 6 calls (b) The marks obtained in mathematics by 1000 students is normally distributed with mean 78% and standard deviation 11%. Determine i. how many students got marks above 90% ii. what was the highest mark obtained by the lowest 10% of the student iii. within what limits did the middle of 90% of the students lie [8+8]
4. Samples of size 2 are taken from the population 4, 8, 12, 16, 20, 24 without replacement. Find (a) mean of the population (b) standard deviation of population (c) the mean of sampling distribution of means (d) standard deviation of sampling distribution of means.
5. (a) A lady stenographer claims that she can take dictation at the rate of 118 words per minute can we reject her claim on the basis of 100 trials in which she demonstrates a mean of 116 words and a S.D of 15 words. (b) In a large consignment of oranges a random sample of 64 oranges revealed that 14 oranges were bad. If it reasonable to ensure that 20% of the oranges are bad? [8+8]
6. (a) The measurements of the output of two units have given the following results. Assuming that both samples have been level whether the two populations have the same varience. Unit-A Unit-B 14.1 10.1 14.7 13.7 14.0 14.0 14.5 13.7 12.7 14.1
(b) The following are the samples of skills. Test the signi?cant di?erence between the means at .05 level. [8+8] Sample-I Sample-II 74.1 77.7 74.4 74 73.8 70.8 74.9 74.2 70.4 69.2 72.2
7. (a) Fit the curve y = aebx to the following data x: 0 1 2 3 4 5 6 7 8 y: 20 30 52 77 135 211 326 550 1052 (b) Fit a second degree polynomial to the following data, taking x as independent variable: [8+8] x: 1 2 3 4 5 6 7 8 9 y: 2 6 7 8 10 11 11 10 15
8. (a) A sample of 12 fathers and their eldest sons gave the following data about their height in inches calculate the coe?cient of rank correlation. [8+8] Fathers 65 63 67 64 68 62 70 66 68 67 69 71 Sons 68 66 68 65 69 66 68 65 71 67 68 70 (b) Given that x = 4y + 5 and y = k x +4 are the regression lines of x on y and y on x, respectively, show that 0 = k = 25. If k = 0.10 actually, ?nd the means of the variables x and y and also their coe?cient of correlation.
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