Expected Value Exercises: This is the second part of the two-part exercise set. 9. (a) The game is to flip a coin. If you get heads, you win two units, if tails, you lose a unit. Then let the random variable X be your win. Find the expected value p = E(X). (b) Next assume that the coin is not fair, say P(heads)= 49 and P(tails)= 51. Find E(X). 10. What is the expected value of a one dollar insurance bet from a six deck shoe. (There are 6(52) cards in the shoe, less the ace that the dealer has up) 11. What is the expected value of a one dollar insurance bet off the top from a single deck where you and your 2 neighbors all have small cards (total of 3 players and dealer ace up)? 12. Lottery. A lottery ticket costs 5 dollars. If you win, you are paid 11 million dollars plus you keep the original 5 dollars. The probability of winning is one out of a 1,000,000. What the expected value of the lottery (round to nearest cent)? 13. European Roulette is the same as American Roulette, but there is only one 0, as opposed to () and (0. So there the probability of winning a bet on a single number is 1/37 with payoff odds of 35:1. Find the expected value as a percentage of the amount bet. 14. Find the expected value of a "red" bet in American Roulette. Half the spots 1...36 are red and half of them are black. The 0 and 00 are neither red nor black. You win a unit if you get red and lose a unit if you don't get red 15. Suppose you bet one unit a roll two dice and you win 2 units if you get a total of 12 (your bet is returned) lose the one unit if you get a total of 2, and push (tie) otherwise, Find the expected value of this bet