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 / = 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 0 and 00. 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