Let f(x,y) be a joint probability density, that is, f(x,y) dxdy is the probability that X lies between x and x + dx and Y lies between y and y + dy. If X and Y are independent, then

If X and Y are independent, show that the mean and variance of their sum is equal to the sum of the means and variances, respectively, of X and Y; that is, show that if W= X+Y, then