Binomial Probability Function-ECO6416

Binomial Probability Function-ECO6416 - Binomial...

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Binomial Probability Function An important class of decision problems under uncertainty involves situations for which there are only two possible random outcomes. The binomial probability function gives probability of exact number of “successes" in n independent trials, when probability of success p on single trial is a constant. Each single trial is called a Bernoulli Trial satisfying the following conditions: 1. Each trial results in one of two possible, mutually exclusive, outcomes. One of the possible outcomes is denoted (arbitrarily) as a success, and the other is denoted a failure. 2. The probability of a success, denoted by p, remains constant from trial to trial. The probability of a failure, 1-p, is denoted by q. 3. The trials are independent; that is, the outcome of any particular trial is not affected by the outcome of any other trial. The number of ways of getting r successes in n trials is: P (r successes in n trials) = n C r . p r . (1- p) (n-r) = n! / [r!(n-r)!] . [p r . (1- p) (n-r) ].
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Binomial Probability Function-ECO6416 - Binomial...

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