# Expand Your Knowledge: Negative Binomial Distribution

Expand Your Knowledge: Negative Binomial Distribution Suppose you have binomial trials for which the probability of success on each trial is and the probability of failure is = 1 – p. Let be a fixed whole number greater than or equalto 1. Let be the number of the trial on which the kth success occurs. This means that the first  k – 1  successes occur within the first – 1 trials, while the kth success actually occurs on the nth trial. Now, if we are going to have successes, we must have at least trials. So, n k= 1, = 2,  . . . and is a random variable. In the literature of mathematical statistics, the probability distribution for is called thenegative binomial distribution.

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