5. (24 points) (OS exercise 3.36, modied) The game of European roulette involves spinning a wheel with 37 slots: 18 red, 18 black, and 1 green. A ball is spun onto the wheel and will eventually land in a slot, where each slot has an equal chance of capturing the ball. You can place bets on red or black. If the ball lands on your color, you double your money. If it lands on another color, you lose your money. Each round of the game is independent. Let X be your winnings from a $1 bet. Throughout this problem, we ignore the cost of the bet when computing winnings, so that your winnings will always be a nonnegative number. 5.1. What is fx(2)? 5.2. What is E(X)? 5.3. What is sd(X)? Round your answer to four significant gures. 5.4. Suppose you bet $3 on a single round. What is the expected value of your winnings? 5.5. Suppose you bet $3 on a single round. What is the standard deviation of your winnings? Round your answer to four significant gures. 5.6. Suppose you bet $1 on three different rounds. What is the expected value of your total winnings for the three rounds? 5.7. Suppose you bet $1 on three different rounds. What is the standard deviation of your total winnings for the three rounds? 5.8. Is the risk of betting $1 in three different rounds greater than, less than, or the same as betting $3 on a single round