Show that the moment generating function (mgf) for the binomial distribution is m(t) = (1 + e t ) n , and use

Show that the moment generating function (mgf) for the binomial distribution is m(t) = (1 – π + πe^t)ⁿ, and use it to obtain the first two moments. Show that the mgf for the Poisson distribution is m(t) = exp{µ[exp(t) – 1]}, and use it to obtain the first two moments.