3. A shuttle operator has sold 20 tickets to ride the shuttle. All passengers (ticket holder) are independent of each other, and the probability that a passenger is part of the frequent rider club is 0.65 (65% chance they are part of the group and 35% chance they are not). Let X be the number of passengers out of the 20 that are part of the frequent rider club.

a. Say each passenger is charged $3.00 for their tickets. What is the expected revenue? What is the variance of the revenue?

b. Now say each passenger in the frequent rider club are charged $2.00 for their tickets and the regular passengers (not in the frequent rider club) are charged $4.50 for their tickets. What is the expected revenue?

c. Let Yi be an indicator (yes or no) if the i-th passenger is in the frequent rider club (for i=1,2,...,20). What type of distribution does Yi follow and what is its parameter?