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Posted By: kondapalli Member Level: Gold Posted Date: 07 May 2008
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2007 Jawaharlal Nehru Technological University B.Tech Computer science and engineering PROBABILITY AND STATISTICS setno4 Question paper
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1. (a) Define a random experiment, sample space, event and mutually exclusive
events. Give examples of each.
(b) Box A contains 5 red and 3 white marbles and box B contains 2 red and 6
white marbles.
i. If a marble is drawn from each box, what is the probability that they are
both of the same colour? [8+8]
2. (a) Let X denote the minimum of the two numbers that appear when a pair of
fair dice is thrown once. Determine the
i. discrete probability distribution
ii. expectation
iii. variance.
(b) Show that if p is small and n is large, then the binomial distribution B(n,p)
is approximated by the Poisson distribution. [8+8]
3. (a) Average number of accidents on any day on a national highway is 1.8. Deter-
mine the probability that the number of accidents are
i. at least one
ii. at most one
(b) If X is a normal variate, Find the probability
i. to the left of z = -1.78
ii. to the right of z = - 1.45
iii. corresponding to - 0.80 z 1.53
iv. to the left of z= - 2.52 and to the right of z= 1.83. [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
(b) standard deviation of population
(c) the mean of sampling distribution of means
(d) standard deviation of sampling distribution of means. [16]
5. (a) In a study of an automobile insurance a random sample of 80 body repair
costs had a mean of Rs. 472.35 and a standard deviation of Rs 62.35. If x is
used as a point estimate to the true average repair costs, with what confidence
we can assert that the maximum error doesn’t exceed Rs. 10? Find also the
confidence interval with that confidence.
(b) A manufacturer of electric bulbs claims that the percentage defectives in his
product doesn’t exceed 6. A sample of 40 bulbs is found to contain 5 defectives.
Would you consider the claim justified? [8+8]
6. The following data gives the fields of interest and attitude to religion:
Arts & Commerce Science & Engineering Total
Conformist 109 51 160
Non-Conformist 23 17 40
Total 132 68 200
Examine whether the field of interest and attitude to religion are associated. [16]
7. (a) Derive normal equations to fit the curve y = ax + bx2
(b) Obtain a relation of the form y = a. (b)x for the following data by the method
of least squares. [6+10]
x 2 3 4 5 6
y 8.3 15.4 33.1 65.2 17.4
8. (a) The following table gives experimental values of the three variates X,Y and Z.
Fit a multiple regression of the type Z = a X + ßY.
X 1 2 3 5
Y 1 3 4 2
Z 7 18 25 23
(b) The following are the marks obtained by 12 students in Economics and Sta-
tistics:
Economics(x) 78 56 36 66 25 75 82 62
Statistics(y) 84 44 51 58 60 68 62 58
Compute the Spearman rank correlation coefficient between x and y. [8+8]
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