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PART - B
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(Answer all five units, choosing one question from each unit)
UNIT - I
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2 (a) If A and B are two events with P(A) = 1/2, P(B) = 1/4, P(A ∩ B) = 1/8, then find P(A / B), P(B / A), P(A / A U B), P(A U B)
(b) State and prove Baye’s theorem.
OR
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3 A problem in statistics is given to three students A, B, C whose chances of solving it are 1/2, 1/3, 1/4 respectively. What is the probability that the problem will be solved?
UNIT - II
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4 (a) A random variable X has the following probability function.
X 0 1 2 3 4 5 6 7 P(x) 0 k 2k 2k 3k k2 2k2 7k2+k Determine (i) k (ii) Evaluate P(X<6), P(X≥6), P(0<X<5)
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(b) Find the moment generating function of the exponential distribution f(x) = (1/c)e(-x/c) , 0 ≤ x < ∞ and hence find its mean and variance.
OR
5 Out of 800 families with 5 children each, how many would you expect to have (a) 3 boys (b) at least one boy (c) no girls (d) all girls? Assume equal probabilities for boys and girls.
UNIT - III
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6 (a) Define the terms: i) Population ii) Sample iii) Parameter iv) Statistic.
(b) A population consists of the four numbers 3, 7, 11, 15. Consider all possible samples of size 2 which can be drawn with replacement from the population. Find the population mean and standard deviation, and mean and standard deviation of the sampling distribution of means.
OR
7 The mean life time of 100 fluorescent light bulbs produced by a company is computed to be 1570 hours with a standard deviation of 120 hours. If μ is the mean life time of all the bulbs produced by the company, test the hypothesis μ = 1600 hours against the alternative hypothesis μ ≠ 1600 hours, using a 5% level of significance.
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UNIT - IV
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8 (a) A random sample of size 16 values from a normal population showed a mean of 53 and a sum of squares of deviations from the mean equals to 150. Can we assert at 5% level of significance that the population mean is 56?
(b) Two independent samples of sizes 9 and 8 respectively had the following values of the variables. Sample 1: 18, 13, 12, 15, 12, 14, 16, 14, 15 Sample 2: 23, 24, 21, 25, 22, 23, 26, 27. Do the two estimates of population variance differ significantly at 5% level of significance?
OR
9 The following are the number of mistakes made in 4 successive weeks by 4 technicians working for a telephone company:
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Technician 1 2 3 4 A 11 9 10 8 B 7 5 6 4 C 8 12 9 11 D 10 10 8 11 Test whether the differences among the four sample means may be attributed to chance.
UNIT - V
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10 (a) Explain the construction and working of X chart.
(b) What is meant by statistical quality control? Explain its uses.
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OR
11 Construct a control chart for number of defectives for the following data:
Sample No 1 2 3 4 5 6 7 8 9 10 No. of defectives 4 7 2 4 1 7 0 5 4 6 Samples of 100 items were taken.
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