The following summations are related to the Poisson distribution. Evaluate each sum. (a) Given M M K! = exp(c), evaluate K ! exp(-A) (This is the sum of the probabilities in the Poisson *=0 1=0 probability distribution.) KXK (b) Evaluate K! exp(-A) (This is the mean of the Poisson distribution.) *=0 k(k - 1)24 (c) Evaluate k! exp(-A) *=0 (d) Evaluate E k! exp(-A) 2 (e) Evaluate (This is the variance of the Poisson distribu- k! exp(-A) E K! exp(-A) tion.)