In this question, you are asked to walk-through computations that are similar to those in the lecture note and slides, but for a bet on 12 numbers rather than a bet on Black. The probability of winning this bet is 12/38. On the layout table on page 4 of LN4.A, we see that a roulette bet on 12 numbers has a payoff of 2:1, so that a bet of $5 pays $10 when it wins; otherwise, it loses $5 (or "pays" -$5).

(a) Find the expected value, the variance, and the standard deviation of a $5 bet on 12 numbers. (Hint: your expected value should equal that of the $5 bet on Black, but your variance will be larger.)

(b) For a $10 bet on 12 numbers, find the expected value, the variance, and the standard deviation.

(c) By what multipliers does the expected value, variance, and standard deviation change when switching from a $5 bet to a $10 bet on 12 numbers?