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

Answer To find the mean and variance of z by simula ...

Suppose that z = xy, where x and y are independent and normally distributed random variables. The

Question:

Suppose that z = xy, where x and y are independent and normally distributed random variables. The mean and variance of x are µ_x = 10 and σ²_x = 2. The mean and variance of y are µ_y = 15 and σ²_y = 3. Find the mean and variance of z by simulation. Does µz = µ_xµ_y? Does σ²_z = σ²_x σ²_y? Do this for 100, 1000, and 5000 trials.