In a restaurant there are three machines frying chips. At any given moment, at least two...
In a restaurant there are three machines frying chips. At any given moment, at least two of the three machines are working. Otherwise a "STOP" sign must be hung on the machines and it will have to get repaired. Define Yi as the life span of the i-th machine that is distributed as Gamma (3,1) (in the months). Suppose that the machines work independently of each other.
1) Find the density function of Yi. What is the probability that one machine has a life span over two months?
2) Assume that every machine was bought at the same time. What is the probability that the restaurant can run without any repairing for more than two months? Denote the time until its first repair occurs as Z.
3)Find the cumulative distribution function of Z.
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In a restaurant there are three machines frying chips. At any
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