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3. (20 points) A random variable Y is said to have log-normal distribution with parameters u and 02 if Y = 6X , where X N N (,u, 02). In this case we write Y N LN([,L, 02). (a) (3 points) Calculate E(Y). (b) (5 points) Calculate Var(Y). (c) (2 points) For any positive integer n, calculate E(Y"). (d) (10 points) Let Y1 ~ LN(0, 0%), Y2 ~ LN(0, 0%), Y3 ~ LN(0, 0%) and Y1, Y2, Y3 are independent. Calculate Corr(Y1Y2, Y2K). Note: Show your derivation for each part