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Geometric Distribution-ECO6416

# Geometric Distribution-ECO6416 - Geometric Distribution In...

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Geometric Distribution In a sequence of independent and identically distributed Bernoulli (p) trials, the number of trials required to get the 1st success has a Geometric(p) distribution. A Typical Geometric Probability Function If a single event or trial has two possible outcomes, say X i can be 0 or 1 with P(X i =1) = p, the probability of having to observe k trials before the first "one" appears is given by the geometric distribution. The probability that the first "one" would appear on the first trial is p. The probability that the first "one" appears on the second trial is p(1-p), because the first trial had to have been a zero followed by a one. By generalizing this procedure, the probability that there will be k-1 failures before the first success is: P (X = k) = (1 –p) k-1 p This is the geometric distribution. A geometric distribution has a mean of 1/p and a variance of (1-p)/p 2 . Application: A manufacturing process is monitored. As each product exits the process line, it is tested for defective versus non-defective. On the first defect, the process is stopped for re-

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