American roulette involves spinning a wheel with 38 slots: 18 red, 18 black, and 2 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. Gamblers can place bets on red or black. If the ball lands on their color, they double their money. If it lands on another color, they lose their money. Suppose you bet $1 on red. Let X be the random variable indicating your winnings after one game. Let Xi be the winnings at the ith game, with i = 1, 2, 3 (see above), and consider the new random variable W = X1 + X2 + X3, that indicates the total amount won or lost: each of the Xi's has the probability distribution explained for X. The three Xi's are independent of one another. a) What is the Range(W)? b) What is the probability distribution of W? Sketch a histogram for it. c) Now compute E(W) and Var(W) from the probability distribution that you found.