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2. The Pareto random variable with parameters a > 0 and B >0 has probability density function (a) Verify that fx is a density function. (b) Find P[X> 3a) (c) Find the mean and variance of X. What restriction do you have on 3 in computing the mean and variance (a different restriction for each)? (d) Use the probability transform to simulate 1000 Pareto random variables with α-1 and β-5 and find their sample mean and variance. Compare this to the values in part (c

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