Two different computer systems are monitored for a total of n weeks. Let Xi denote the number of breakdowns of the first system during the ith week, and suppose the Xi’s are independent and drawn from a Poisson distribution with parameter μ1. Similarly, let Yi denote the number of breakdowns of the second system during the ith week, and assume independence with each Yi Poisson with parameter μ 2. Derive the mle’s of μ 1, μ 2, and μ 1 – μ 2. [Hint: Using independence, write the joint pmf (likelihood) of the Xi’s and Yi’s together.]
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