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Probability distribution of the time

Suppose that earthquakes occur in the western U.S. In accordance with a Poisson distribution with a mean of 2 per week. A) find the probability that at least 3 earthquakes occur during the next 2 weeks. B) find the probability distribution of the time, until the next earthquake.

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## Q : Generate a random variable

Suppose we generate a random variable X in the following way. First we flip a fair coin. If the coin is heads, take X to have a Unif(0,1) distribution. If the coin is tails, take X to have a Unif(3,4) distribution.