Problem
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.
The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.