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 m1. 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 m2.

Derive the mle’s of m1, m2, and m1 m2. [Hint: Using independence, write the joint pmf (likelihood) of the Xi

’s and Yi

’s together.]