Another form of bet for roulette is to bet that a specific number (say 17) will turn up. If the ball stops on your number, you get your dollar back plus 35 dollars. If not, you lose your dollar. You place a 1-dollar bet on the number 17. Let Y be your winnings. Define S and calculate the values of P ( Y ) , E ( Y ) and V ( Y ) .
Compare your answers from exercise 3, E ( X ) , E ( Y ) , and V ( X ) , V ( Y ) . What do these computations tell you about the nature of your winnings if you make a sequence of bets, betting each time on a number versus betting each time on a color?