For a sequence of independent Bernoulli trials, let y = the number of successes before the kth failure. Show that y has the negative binomial distribution, f(y; ????, k) = Γ(y + k)

Γ(k)Γ(y + 1)????y

(1 − ????)

k

, y = 0, 1, 2,… .

(The geometric distribution is the special case k = 1.) Relate ???? to the parameters ???? and k in the parameterization (7.8).