Discuss the below:
Q: Consider the experiment of observing a sequence of Bernoulli trials until exactly r successes occur. Let the r.v. X denote the number of trials needed to observe the rth success. The r.v. X is known as the negative binomial r.v. with parameter p, where p is the probability of a success at each trial.
The pmf of the negative binomial distribution is given by:
px(x)= ( x-1 r-1) py(1-p)x-y