Could please explain how is this question answered step by step. Thank you.

2. Let X ~ Poisson(A) for certain > > 0. For each of the following cases determine a function f : {0, 1, 2, . . .} - R such that the corresponding identity applies. The function f cannot depend on 1. (a) E(f (X) ) = 7. (b) E(f (X ) ) = 1. (c) E(f (X) ) =13. ( d) E(f ( X ) ) = ell (e) E(f(X)) = _, when 0