4. 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. (Assume 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. [3 marks]

b.True or false: Ten customers are selected at random. The total number of store visits of the 10 customers will be ten times of the expected value we calculated in part (a) above. [2 marks]

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