You are thinking of betting $450,000 on Donald Trump winning the 2020 Presidential Election at predictit.org. Currently, Trump's share costs $.45. It will pay $1.00 if Trump wins the election. Your current wealth is $1,000,000. Let T denote "Trump wins". You are fully confident that Pr(T) = 5. Let X denote your future wealth when the result is officially determined on November 3, 2020. a. Suppose that you go ahead and bet $450,000 on Trump. Write down the probability distribution of X, assuming that Pr(T) = 5. Calculate E(X). b. Suppose that your utility function is logarithmic (i.e., U(x) = In(X)). Is U(.) linear, concave, or convex function? Calculate E(U(X)), assuming that Pr(T) = 5. Should you go head and bet $450,000? What is the minimum probability of Trump winning the election in order for you to go ahead and bet $450,000?