24. Two different computer systems are monitored for a total of n weeks. Let Xi denote the number of breakdowns of the rst system during the ith week, and suppose the Xi s are independent and drawn from a Poisson distribution with parameter l1. 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 l2.

f 1x; u2  e 1u  12xu 0 x

1 0 otherwise gx2i x  28.0  16,500 V1X2  b2511  2/a2  311  1/a2 426 E1X2  b # 11  1/a2 Derive the mle s of l1, l2, and l1 l2. [Hint: Using independence, write the joint pmf (likelihood) of the Xi s and Yi s together.]