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In: Statistics and Probability

Simulate 50000 exponential random numbers having rate 3. (a) Find the proportion of these numbers which...

Simulate 50000 exponential random numbers having rate 3. (a) Find the proportion of these numbers which are less than 1. Compare with the probability that an exponential random variable with rate 3 will be less than 1. (b) Compute the average of these numbers. Compare with the expected value. (c) Calculate the variance of this sample, and compare with the theoretical value.

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