Special distributions; negative binomial distribution.

4.5.6. Let the random variable X denote the number of trials in excess of r that are required to achieve the rth success in a series of independent trials, where p is the probability of success at any given trial. Show that ktr-1 Px ( k ) = k p'(1 - p)", k = 0, 1, 2, . . . (Note: This particular formula for py (k) is often used in place of Equation 4.5.1 as the definition of the pdf for a negative binomial random variable.)