4. [4 points] Customers at a restaurant pay with a credit card (CC), debit card (DC), or cash(C). Assume that successive customers make independent choices, with P(CC)=.5, P(DC)=.2, and P(C)=.3.
a). [2 points] Among the next 100 customers, what are the mean and variance of the number who pay with a debit card? Please define the random variable you are using to answer this question and write down the distribution your defined variable follow.
b). [2 points] Among the next 100 customers, what are the mean and variance of the number who don't pay with cash? Please define the random variable you are using to answer this question and write down the distribution your defined variable follow.