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2007 Anna University Chennai B.Tech Computer Science and Engineering Probability and Statistics Question paper



Course: B.Tech Computer Science and Engineering   University/board: Anna University Chennai





MODEL QUESTION PAPER

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,
find
i. P(A/B)
ii. P(A \Bc )
(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) = k2 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 be-
tween 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 re-
placement. Find
(a) mean of the population
1 of 2
(b) standard deviation of population
(c) the mean of sampling distribution of means
(d) standard deviation of sampling distribution of means. [16]
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 variance.
Unit-A 14.1 10.1 14.7 13.7 14.0
Unit-B 14.0 14.5 13.7 12.7 14.1
(b) The following are the samples of skills. Test the significant difference between
the means at .05 level. [8+8]
Sample-I 74.1 77.7 74.4 74 73.8 -
Sample-II 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 coecient 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, find the means
of the variables x and y and also their coeent of correlation.
? ? ? ? ?
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