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# Mid2Examples-answers-all - Question 1(a(3 pts A particular...

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Question 1 (a) (3 pts) A particular type of device is manufactured and shipped to stores. Due to problems with the manufacturing process, some devices do not work. Say we manufacture 20 devices and ship them to two stores. Store A receives 8 devices and Store B receives 12 devices. Assume we know that 2 of the 20 devices do not work. (i) Let X = the number of working devices received by Store A. What is the probability distribution of the random variable X ? You need to specify the name of the distribution, all necessary parameters, the possible values of X . Answer: X has the hypergeometric distribution with parameters M = 18, the total number of successes in the population, N = 20, the population size and n = 8 the sample size: X HG( n = 8 , M = 18 , N = 20) . Note that the distribution is defined (non-zero) for x = 6 , 7 , 8 because Store A can’t receive, say, only 5 working devices because that would mean it received 3 non-working devices, which is impossible. (ii) Still assuming that 2 of the 20 devices do not work, what is the probability that Store A receives 8 working devices? Answer: This can be answered using the pdf of the hypergeometric distribution: P ( X = 8) = ( 18 8 )( 2 0 ) ( 20 8 ) = 18! / (8!10!) 20! / (8!12!) = 18! × 12!

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