What Geometric distrib is
The geometric distribution is a type of probability distribution that models the number of Bernoulli trials (success/failure) needed for a single success. It is used to describe processes in which the probability of success is constant and the outcomes of the trials are independent.
Steps for Geometric Distribution:
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Determine the probability of success, p. This is the same for each trial.
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Determine the probability of failure, q. This is 1 - p.
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Determine the probability of r successes in a row, P(r successes). This is p^r.
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Determine the probability of r+1 failures in a row, P(r+1 failures). This is q^(r+1).
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Calculate the probability of r successes in a row followed by one failure, P(r successes, 1 failure). This is the product of the probabilities of the successes and the failure, p^r * q.
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Calculate the probability of r successes, P(r successes). This is the sum of the probabilities of r successes followed by 1, 2, 3, etc., failures.
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Calculate the cumulative probability of r successes. This is the sum of the probabilities of 0, 1, 2, 3, etc., successes.
Examples
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Geometric distributions are often used to model the number of Bernoulli trials needed to get a success. For example, a customer service rep could use a geometric distribution to model how many customer calls it takes to solve a problem.
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Geometric distributions are also used to model the number of independent events before a specified event occurs. For example, a company could use a geometric distribution to model how many online advertising clicks it takes to get a purchase.