Problem 3 [15 points = 4 + 6 + 5] Two stocks are considered. The changes per day for a share price are denoted as X and Y, respectively. Analysts assume that the random variables, X and Y are independent, and their marginal distributions are listed below. Distribution of X is: Distribution of Y is: P[X = 2] = 0.3, P[X = 0] = 0.2, and P[X = 3] = 0.5 PY = -3] = 0.2, P[Y = 0] = 0.4, and P[Y = 2] = 0.4 1. Find expectations for X and Y E[X] = E[Y] = 2. Derive variances for each of these variables Var [X] = Var [Y] = 3. For a variable, T = X + 2Y, determine its expectation and variance = E[T] Var [T] = Solution =