A coin has probability p of landing heads. You are offered a bet in which you will be paid $21 if the first head occurs on the jth flip.
(a) What is the expected value of this bet when p = 1/2?
(b) Suppose that your expected utility function is u(x) = lnx. Express the utility of this game to you as a sum.
(c) Evaluate the sum. (This requires knowledge of a few summation formulas.)
(d) Let wo be the amount of money that would give you the same utility you would have if you played this game. Solve for wo.