PASCAL DISTRIBUTION - Quantitative Techniques for management

In binomial distribution, we derived the probability mass function of the number of successes in n (fixed) Bernoulli trials. We can also derive the probability mass function of the number of Bernoulli trials needed to get r (fixed) successes. This distribution is known as Pascal distribution. Here r and p become parameters while n becomes a random variable.

We may note that r successes can be obtained in r or more trials i.e. possible values of the random variable are r, (r + 1), (r + 2), ...... etc. Further, if n trials are required to get r successes, the nth trial must be a success. Thus, we can write the probability mass function of Pascal distribution as follows:


It can be shown that the mean and variance of Pascal distribution are r/p and rq/p2respectively. This distribution is also known as Negative Binomial Distribution because various values of P(n) are given by the terms of the binomial expansion of pr(1 - q)- r

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