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. Vimat type of distribution does X follow? Write the probability mass function (f name its parameters. b. IA,mat is the expected number of passengers that are part of the frequent rider club. Interpret this value for the shuttle operator (in a sentence or two). c. IA,mat is the probability that exactly 10 ticket holders are part of the frequent rider club? Write out the theoretical form and use R to compute a numerical value. d. IA,mat is the probability that majpvity.qf ticket holders are part of the frequent rider club? Write out the theoretical form and use R to compute a numerical value. e. Say each passenger is charged $3.00 for their tickets. IA,mat is the expected revenue? IA,mat is the variance of the revenue? f. 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. IA,mat is the expected revenue? g. Let Yi be an indicator (yes or no) if the i-th passenger is in the frequent rider club (for 2 ...,20). IA,mat type of distribution does Yi follow and what is its parameter?