Negative Binomial Distribution-ECO6416

Negative Binomial Distribution-ECO6416 - Negative Binomial...

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Negative Binomial Distribution This is an extension of the geometric distribution, describing the waiting time until r "ones" have appeared. The probability of the r th "one" appearing on the k th trial is given by the negative binomial distribution: P (X = k) = r-1 C k-1 p r-1 (1 –p) k-r p in other words, the first part is the probability of r-1 success in the previous k-1 trails as a binomial probability, the last tem is the probability of success. The following is a Negative Binomial probability function with parameters (r = 6 , k= 30, p = 0.5): A Negative Binomial Probability Function A negative binomial distribution has: mean = r/p and variance = r(1-p)/p 2 Application: Suppose we are at a rifle range with an old gun that misfires 5 out of 6 times. Define ``success'' as the event the gunfires and let X be the number of failures before the third success. Then X has a negative binomial with parameters (3, 1/6). The probability that there are 10 failures before the third success is given by:
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This note was uploaded on 10/04/2011 for the course ECO 6416 taught by Professor Staff during the Spring '08 term at University of Central Florida.

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