What happens if the correlation is not zero? Suppose that X is a random variable with mean 30 and standard deviation 4. Also suppose that Y is a random variable with mean 50 and standard deviation 8. Assume that the correlation between X and Y is 0.5. Find the variance and the standard deviation of the random variable Z for each of the following cases. Be sure to show your work (a) Z 35 10X. (b) Z 12x 5. (c) Z- X + Y. (d) Z-X -Y (e)Z-2X 2Y.