Let X be a Poisson random variable with parameter . a. Show that by using the result of Theoretical Exercise 4.15 and the relationship between

Let X be a Poisson random variable with parameter λ.

a. Show that 

by using the result of Theoretical Exercise 4.15 and the relationship between Poisson and binomial random variables.

b. Verify the formula in part (a) directly by making use of the expansion of e^-λ + e^λ.

A family has children with probability qpⁿ, n ≥ 1, where α ≤ (1 - p)/p.

P{Xis even} s even} =1+e-21