Show that the moment generating function of the negative binomial distribution is M(t) = p r [1 − (1 − p)e t ] −r . Find the mean and the variance of this distribution. Hint: In the summation...

Show that the moment generating function of the negative binomial distribution is M(t) = p^r[1 − (1 − p)e^t
]
^−r. Find the mean and the variance of this distribution.

Hint: In the summation representing M(t), make use of the negative binomial series.