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PS_8_QUESTIONS

# PS_8_QUESTIONS - 0.26 0.91 0.62 0.11 0.45 0.72 0.28 0.85...

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IE 306 PS#8 17.04.09 1. Develop an acceptance-rejection technique for generating a geometric random variable, X , with parameter p on the range {0, 1, 2, }. [ Hint: X can be thought of as the number of trials before the first success occurs in a sequence of independent Bernoulli trials.] 2. Develop a technique for generating a binomial random variable, X , using the convolution technique . [ Hint: X can be represented as the number of successes in n independent Bernoulli trials, each success having probability p. Thus, , where P( =1) =p and P( =0) =1-p.] 3. Develop a generator for a triangular distribution with range (1, 10) and mean at using inverse transformation technique . 4. Suppose i.i.d. with p.d.f. , . (a) Find the maximum likelihood estimator for . (b) Consider the following n = 24 i.i.d. observations. 0.59 0.38 0.46 0.69 0.09 0.93 0.69 0.16 0.90 0.18 0.29 0.98 0.69 0.26
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Unformatted text preview: 0.26 0.91 0.62 0.11 0.45 0.72 0.28 0.85 0.75 0.31 0.27 Conduct a - goodness-of-fit test to see if the data arises from the p.d.f. given in part (a). Use α = 0.05 and k = 3 equal-probability intervals. 5. Records pertaining to the monthly number of job-related injuries at an underground coal mine were being studied by a federal agency. The values for the past 100 months were as follows: Injuries per Month Frequency of Occurrence 0 35 1 40 2 13 3 6 4 4 5 1 6 1 (a) Find the maximum likelihood estimator for the λ parameter of Poisson distribution. (b) Apply the chi-square test to these data to test the hypothesis that underlying distribution is Poisson. Use a level of significance α = 0.05. (c) Apply the chi-square test to these data to test the hypothesis that underlying distribution is Poisson with mean 1.0. Use a level of significance α = 0.05....
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