Neg Binomial

Neg Binomial - Negative Binomial Distribution A discrete...

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Negative Binomial Distribution A discrete random variable Y is said to have a negative binomial distribution if The experiment involves independent and identical trials. Each trial has two possible outcomes, success and failure. The probability of success on each trial is the same, p . Therefore, the probability of failure on each trial is 1 - p = q . The experiment is repeated until the r th success occurs. The random variable Y is deFned as the number of the trial on which the r th success occurs. The parameters for the negative binomial random variable Y are the probability of success on each trial p and the number of the r th success. The probability distribution function of the negative binomial random variable Y is p ( y ) = p y - 1 r - 1 P p r (1 - p ) y - r for y = r, r + 1 , r + 2 , . . . The theoretical mean of the negative binomial random variable Y is μ = E ( Y ) = r p The variance of the negative binomial random variable Y is
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Neg Binomial - Negative Binomial Distribution A discrete...

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