4. Let X1 and X2 be independent random variables with the following density function: f (x) - de 1x for x > 0, 1 > 0 otherwise Find the joint density function of Y, = X, + 2X2 and Y2 - X2 with ox Ox1 dy1 dy 2 Ox 2 Ox 2 ay1 [Total: 12 Marks] 5. a. A coin is flipped 3 times and the probability of getting a head is twice as likely to occur as a tail. Let X be the number of heads obtained. i. Compute the kth moment of X. (5 Marks) ii. Find the mean and variance of X using this kth moment. (5 Marks) b. Let X be a random variable with moment generating function Mx(t) - (2+ Find the variance of X. (8 Marks) [Total: 18 Marks]