Recall Exercise 11.5.10 on betting on red on the roulette wheel. 

a. Write out the probability distribution of the payout for betting $1 on red twice. 

b. Find the mean of your probability distribution from part (a). 

c. Find the standard deviation of your probability distribution from part (a).

Data from Exercise 11.5.10

An American roulette wheel has numbers 1 through 36, where the even numbers are black and odd numbers are red. There are also numbers 0 and 00, which are green. The wheel is spun and a ball will randomly land on one of these 38 numbers. Suppose you plan always to bet $1 on red. If it lands on red, you will gain $1 (payout = $1). If it does not land on red, you will lose $1 (payout = −$1).