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FPSC · CSS 2014

Statistics

100 marks · 3 hours · 2 questions
This paper Statistics · all yearsQ. 2 · Red, 3 White, 1 Blue…Q. 9 · Writer short NOTES on the…With this paper← 20132016 →
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Part II

Q. 2

Red, 3 White, 1 Blue P ( 2 , 3 , 1 ) = 6!2!3!1!(0.5)2(0.3)3(0.2)1P(2,3,1)=\frac{6!}{2!3!1!} (0.5)^2 (0.3)^3 (0.2)^1 P ( 2 , 3 , 1 ) = 60 P(2,3,1)=60×0.25×0.027×0.2=0.081P(2, 3, 1) = 60 \times 0.25 \times 0.027 \times 0.2 = \mathbf{0.081} (iii) Probability: 2 of each color (2 Red, 2 White, 2 Blue) P ( 2 , 2 , 2 ) = 6!2!2!2!(0.5)2(0.3)2(0.2)2P(2,2,2)=\frac{6!}{2!2!2!} (0.5)^2 (0.3)^2 (0.2)^2 P ( 2 , 2 , 2 ) = 7208×0.25×0.09×0.04P(2,2,2)=\frac{720}{8} \times 0.25 \times 0.09 \times 0.04 P ( 2 , 2 , 2 ) = 90 P(2,2,2)=90×0.0009=0.081P(2, 2, 2) = 90 \times 0.0009 = \mathbf{0.081} 3

  1. (a)An irregular six faced die is thrown and the expectation that in 10 throws it will give five even numbers is twice the expectation that it will give four even numbers how many times 10000 sets of 10 throws would you expect it to give one even number? [4]
  2. (b)Drive the Poisson distribution as the limiting form of the binomial distribution, stating clearly the assumptions you make. [4]
  3. (c)To avoid detection at customs, a traveller has placed seven narcotic tablets in a bottle containing nine vitamin pills that are similar in appearance. If the customs official selects 3 of the tablets at random for analysis, what is the probability that the traveller will be arrested for illegal possession of narcotics? [4]
  4. (d)A doctor receives an average of 5 telephone calls from 9 p.m. until 9 a.m. the next morning. Assuming arrivals of calls are a Poisson process, what is the probability that the doctor will not be disturbed by a call if she goes to bed 10 p.m. and rises at 6 a.m. [4]
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Q. 9

Writer short NOTES on the following:

  1. (a)Multiple and Partial correlations [4]
  2. (b)Comparison of Stratified and cluster Sampling schemes [4]
  3. (c)Maximum likelihood estimator [4]
  4. (d)Properties of a good estimator [4]
(16)

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