Show that the probability density function of a negative binomial random variable equals the probability density function of a geometric random variable when r = 1. Show that the formulas for the mean...

Show that the probability density function of a negative binomial random variable equals the
probability density function of a geometric random variable when r = 1. Show that the formulas
for the mean and variance of a negative binomial random variable equal the corresponding results
for a geometric random variable when r = 1.