Question: Two different computer systems are monitored for a total of n weeks. Let X, denote the number of breakdowns of the first system during the

Two different computer systems are monitored for a total of n weeks. Let X, denote the number of breakdowns of the first system during the ith week, and suppose the X's are independent and drawn from a Poisson distribution with parameter . Similarly, let Y, denote the number of break- downs of the second system during the ith week, and assume independence with each Y, Poisson with parameter . Derive the mle's of , and . [Hint: Using independence, write the joint pmf (likelihood) of the X's and Y's together.]

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