1.20 Show that the moment generating function (mgf) is (a) m(t) = (1 - + ') for the binomial distribution, (b) m(t) = exp{u[exp(t)

1.20 Show that the moment generating function (mgf) is

(a) m(t) = (1 - π + πε')" for the binomial distribution,

(b) m(t) = exp{u[exp(t) - 1]} for the Poisson distribution.

For each distribution, use them to obtain the first two moments and to show a reproductive property.