Recall Exercise 11.5.11 on betting on the number 23 on the roulette wheel. 

a. Write out the probability distribution 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 11.5.11

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. Suppose you plan always to bet $1 on the number 23 (your lucky number). If it lands on 23, you will gain $35. If it does not land on 23, you will lose $1.