2. Suppose X has range (0, +00) and probability density function (PDF) f(x) = 2e-2 (Total 20 marks, 4 marks each) (a) Find the cumulative distribution function (CDF) of X. (b) Find the mean of X. (c) Find the variance of X. density PPF (d) Assume that Y = X2, find the probability ass function (PMF) and cumulative distribution function (CDF) of Y. (e) Assume that Y = X2, find the mean of Y. 3. Given So, the stock price at time T is =Soe(r-20)T+0BT, where r and o are constant and BT is a Brownian motion with mean zero and variance T. Given the risk-neutral valuation formula, ST = Co = e-TE [CT], where Cr is the payoff function of an option, CT = max(3ST-2K, 0), where K is constant and positive. (Total 20 marks, 10 marks each) (a) Please calculate E[S] where a is a positive integer (i.e., a = 1,2,3...). (b) Please calculate co.