The Geometric Distribution: A \"discrete\" distribution In independent trials, only two outcomes are possible: \"success\" and \"failure.\" For every trial, the probability of \"success\" is p (0,1). The trial on which the first success occurs is a random variable with a \"geometric\" distribution; the probability that the first success occurs at trial x is: Pr(X = x) = f(x) = p (1 - p)x-1, x = 1, 2, 3, ... 1.2 p (0,1) is the probability of \"success\"; 1 - p probability of \"failure.\" Since 0 < p < 1, 1 - p will also be between 0 and 1. p = 0.56 p (0,1) 1 0.8 Pr(X = x) Welcome to Professor Mitchell's interactive geometric distribution worksheet! 0.4 Dp= xi 0.6 0.2 x1 = 2 x1 Z++ x2 = 3 x2 Z++ 0 x x1 Pr(X < xi) 0.56 Pr(X xi) 0.8064 Pr(X = xi) 0.2464 Pr(X xi) 0.44 Pr(X > xi) 0.1936 x2 0.8064 0.91482 0.10842 0.1936 0.08518 2005 Thomas Mitchell, All Rights Reserved Cumulative distribution Probability: Pr(X = x) or every trial, the probability variable with a \"geometric\" (x) = p (1 - p)x-1, x = 1, 2, 3, ... Cumulative distribution Probability: Pr(X = x) v 1.1 / 03.22.05