(a) Now, think in Bayesian terms. Previously PfB} denoted prior probability; and P{B} was a single number between 0 and 1, such as, for example, P(B) = .7. Now, the prior is an entire probability density function f (X) . For example, f (X) is the prior probability density for the event E described above. Assume that\" = '6 =2. Show that this Bayesian prior f (X) is a quadratic. Also, graph this function in Excel as follows: In Column A, set X = 0, and then increment X by .01 in successive rows until you reach X = 1.0. That is, the values in Column A are 0, .01, .02, ...., .99, 1.00. In Column B, calculate the corresponding values of x) . Draw a graph in Excel with X on the horizontal axis and x) on the vertical axis. This prior probability density function represents your beliefs (for whatever reasons) about the probability of event E occmring. At what value of X is the quadratic maximized [which is the expected value of X because of the symmetry of 10W]