The number of times a machine malfunctions per week follows a Poisson distribution. It averages 2 malfunctions per week. (a) What is the probability that it does not malfunction at all in a certain week? (b) What is the variance of the number of times it malfunctions in a certain 52 week period? Hint: If the number of times some thing happens during a given time period exactly follows a Poisson distribution, then the number of times the thing happens during any other given time period also follows a Poisson distribution (with a different parameter). (c) The machine's owner decides she will throw it out when it next malfunctions. What is the probability that she throws it out sometime in the third week after deciding this?
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The number of times a machine malfunctions per week follows a Poisson distribution and the probability that it does not malfunction at all during one week equals e-1/2. What is the expected value of the number of times it malfunctions in a certain 52 week period? What is the variance in the number of times it malfunctions in that 52 week period?
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