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Probability 4 A computer program generates 100 independent Poisson RVs with mean )1. = 2. Let X- denotes the average of these 100 numbers. (a)

Probability 4

A computer program generates 100 independent Poisson RVs with mean )1. = 2. Let X- denotes the average of these 100 numbers. (a) Give the approximate distribution of 2?, with its parameter(s), and explain why this approximation is valid. (b) What is the probability that )E is greater 2.25? (c) What is the probability that X is between 1.80 and 2.95

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