Please help me solve this question with detailed explanation

Consider a Gaussian random variable X, i.e., X ollows a normal distribution with mean it and variance 0': X ~.N'(p,a"). (5) There is a function of X: u(X) = -e"""'1 (6) where v > 0 is a parameter. a. Compare E[u(X}] and u(E[X]). Are they equal? If not, which one is bigger. b. Compute E[u{aX ), where a is a choice variable. c. Show that the optimization problem mytE[u(aX)l (7) is the same as the following one max pa - 190's\". (3) a 2 Hint: The probability density function for normal distribution with mean In and variance o2 m) = aha-\"g. The expected value of a function 9(1'), when a: is a random variable with a probability density function Hz). is iyumxldz