The mean of the sum (or difference) of two independent random variables equals the sum (or difference) of their means, but the variance is always the sum of the two variances. Use random number generation to verify this statement for the case where z = x + y, where x and y are independent and normally distributed random variables. The mean and variance of x are µx = 8 and σ2x = 2. The mean and variance of y are µy = 15 and σ2y = 4. Find the mean and variance of z by simulation, and compare the results with the theoretical prediction. Do this for 100, 1000, and 5000 trials.
