MAT 316 Lecture Notes - Lecture 8: Memorylessness, Probability Distribution, Geometric Distribution
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Situation: you are performing bernoulli trials, the trials are all independent, p(success) = p remains constant for each trial. Note: this is the same situation as the binomial, except that there is not a set number of trials. X = the number of the trial where the first success occurs. Derive the pmf of the geometric (1) distribution. Pmf: p(x) = (1 p)x 1p i{1, 2, 3, }(x) Note: this is not how our textbook defines the geometric distribution, but it is how it defined it in the previous editions and is the one i prefer to use. It is the default value in my notation. About half of books (and also excel) define the geometric the other way, so you need to know it when you see it. In practice, use whichever is easier to work with. Y = the number of failures before the first success occurs. Pmf: p(y) = (1 p)yp i{0, 1, 2 }(y)
