The following problems are associated with the St. Petersburg Game: Suppose the St. Petersburg game is modified such that the payoff function is n 1/3 dollars. Given this, (A) Establish that the expected value of this modified game is finite and determine its value. Why is the expected value finite in this modified St. Petersburg game but infinite if the payoff function is 2^n-1 (B) Suppose there is an entrance fee to play each round of this game, where each round has n 2 10 coin tosses. What must the entrance fee be less than such that your expected value will always be greater than that fee