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4. (30 points) Suppose X~N (30, 144), and W N(40, 225) 4a. If X and W are uncorrelated, find the mean and variance of X 2W 4b. Find the probability that X + 2W > 100. Henceforth, suppose that X and W have a correlation coefficient ρ=-25. 4c. What is the covariance of X and W? 4d. Find the probability that X + 2W 100. 4e. Find the probability that 50 < X + 2W < 120

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