The number of eggs laid on a tree leaf by an insect of a certain type is a Poisson random...

The number of eggs laid on a tree leaf by an insect of a certain type is a Poisson random variable with parameter λ.However, such a random variable can be observed only if it is positive, since if it is 0, then we cannot know that such an insect was on the leaf. If we let Y denote the observed number of eggs, then

where X is Poisson with parameter λ. Find E[Y].