Suppose that X, the number of times a customer goes to a grocery store in a week, is a random variable with probability distribution shown in the accompanying table. (Assuming that no customer goes to the store more than 3 times a week).

x 0 1 2 3

p(X) 0.2 0.4 0.3 0.1

a) Calculate E(X) and explain what the number means.

b) True or false: Ten customers are selected at random. The total number of store visits of the 10customers will be ten times of the expected value we calculated in part (a) above.

c) Suppose the store has a promotion where a customer is given a $2 credit for each visit; and anadditional $3 credit for his/her 3rdvisit in a week (so he/she gets a total of $5 credit on his/her 3rdvisit of the week). Find the probability distribution of Y = Amount of credit the store gives to acustomer in a week.