Bacterial Plates Mutations

Bacterial plates are exposed to radiation. The number of mutations caused by the radiation has a Poisson distribution wth mean $\displaystyle \mu$. We can only observe if a plate has no mutations or at least one. N plates are examined. The number of mutations on each plate can be assumed to be independent of each other.

Let Yi = 0 if the ith plate has no mutations and Yi = 1 if the ith plate has at

least one mutation. Z = $\displaystyle \Sigma$ Yi, i=1....N, is the number of plates with at least one mutation, derive E(Z).