Suppose that z = xy, where x and y are independent and normally distributed random variables. The
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Suppose that z = xy, where x and y are independent and normally distributed random variables. The mean and variance of x are µx = 10 and σ2x = 2. The mean and variance of y are µy = 15 and σ2y = 3. Find the mean and variance of z by simulation. Does µz = µxµy? Does σ2z = σ2x σ2y? Do this for 100, 1000, and 5000 trials.
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