4. Georgie wants to play the crane machine arcade game (the one with the mechanical claw) to win a stuffed animal. He is good at the game, so for each time he plays, there is a 15% chance that he will win a stuffed animal. Assume that each attempt is independent in its outcome. a) Let A be the attempts until Georgie wins his first stuffed animal. What are the distribution, parameter(s), and support of A? b) Find the expected value and variance ofA. c) What is the probability that it takes exactly 6 games for Georgie to win a stuffed animal? cl) What is the probability that it takes at least 6 games until Georgie wins a stuffed animal? e) Georgie has already played 6 games and has not won a stuffed animal, what is the probability that it takes no more than 9 games altogether until he wins a stuffed animal? f) Suppose that it costs $1.25 to play a game and the stuffed animal in the toy store costs $12. On average is it worthwhile for Georgie to play the crane machine game to get the stuffed animal instead of buying one in the toy store? Justify your answer mathematically