Problem 1 (20 points) Answer the following questions: a. WIN Let X1, . .. ,Xn be i.i.d. N(p,a). Find c such that EC ratio). = g (This can be interpreted as a signaltonoise . Let X1, . . . ,Xn be i.i.d. _N(p, 0). Find the joint moment generating function of X and X1 X and use it to show that X' and X1 X are independent. Suppose ln(Y) = ,60 + 31:13 + c, with e N N (0,0). Assume that g, [31, :r are nonrandom. Find the mean and variance of Y. Explain how to match the table of the standard normal distribution with the table of the X2 distribution with 1 degree of freedom. Clearly explain your answer and give a numerical example