7. [14 points total] Let X be a standard Gaussian random variable with mean / and variance oz meaning it has density e 17(3-4) on IE (-00, 00). (a) [7 points] Let Y = ex. Find the density fy(y) of Y and the support of Y. (b) [7 points] Suppose that / = 0. Use the expectation E[Y] = es" to show that P(X > t) 0 for some C > 0. State the value of C' you are using explicitly