Roulette wheels are typically marked with the numbers 1 through 36 plus 0 and 00. Each of these outcomes is equally likely every time the wheel is spun. If you place a bet on any one number and are correct, the payoff is 35:1; that is, if you bet 1, you will receive 36 if you win and nothing if you lose.
a) Suppose that you place a 1 bet on your favorite number. What is the casino's expected profit? What is the standard deviation of this profit for a single bet? Your odds of winning are 1 in 38=0. 0263. We use a weighted average to find the expected casino payoff. If you win the casino looses 35; if you loose the casino gets 1. Casino Payoff =?. ???? * -?? + (? -?. ???) * ? = ?. ??? We then use a the standard deviation formula. SD of payoff is V2 x (-22 - ElPay? f fl) ? + (2 -2) x (? - E Pay? ffi) ?=5 76
a) 7. 89
b) 6. 32
c) 8. 60