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If X has the binomial distribution with n trials and probability p of success on each trial, then possible values of X are 0, 1, 2…n. If k is any one of these values, nknk ( ) P(X = k) =p k (1 – p) n – k

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The expected number of successes and failures are both at least 10

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Arises when we perform independent trials of the same chance process and record the number of trials until a particular outcome occurs.

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inary? The possible outcomes of each trial can be classified as “success” or “failure” ndependent? Trials must be independent; knowing the result of one trial must not have any effect on the result of any other trial rials? The goal is to count the number of trials until the first success occurs uccess? On each trial, the probability p of success must be the same

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Number of trials Y that it takes to get a success Probability distribution of Y with parameter p, probability of a success on each trial. The possible values of Y are 1, 2, 3….

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If Y has the geometric distribution with probability p of success on each trial, then possible values of Y are 1, 2, 3…. If k is any one of these values, P(Y = k) =(1 – p) k – 1 p

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Random Variables. A random variable X is a real valued function defined on the sample space, X : S R. The set { s S : X ( s ) [ a, b ] is an event}.

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