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A fair coin is flipped until a Head appears or until a maximum of three flips. Let Y be the number of flips. Determine the PMF (Probability Mass Function) of Y. Solution In probability theory and statistics, the negative binomial distribution is a discrete probability distribution of the number of successes in a sequence of Bernoulli trials before a specified (non-random) number of failures (denoted r) occur. For example, if we define a \"1\" as failure, and all non-\"1\"s as successes, and we throw a die repeatedly until the third time.

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A fair coin is flipped until a Head appears or until a maximum of three flips. Let Y be the number of flips. Determine the PMF (Probability Mass Function) of Y. Solution In probability theory and statistics, the negative binomial distribution is a discrete probability distribution of the number of successes in a sequence of Bernoulli trials before a specified (non-random) number of failures (denoted r) occur. For example, if we define a "1" as failure, and all non-"1"s as successes, and we throw a die repeatedly until the third time

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