1.

[5 point-s) Suppose a leprechaun wishes to share his gold with you. The number of gold pieces he will share is based on how man};T articles of green clothing you are wearing. Suppose X denotes the number of articles of green clothing you are wearing has the following prof. x D 1 2 3 4 phi} .15 .40 .25 .15 .05 Further suppose the amount he shares with you has the function H {X } = 75X + 15. What is the expected number of gold pieces you will reeeive? (6 points) Suppose you want some chicken from a certain restaurant that sells Chicken of the Kentucky Fried variety. To your horror, there is a chicken shortage! The manager of one of the restaurants tells you that 82% of restaurants have no chicken. You decide to try your luck and keep going to restaurants in this chain until you find one that has chicken left. (The first restaurant where the manager informs you of the shortage does not count as the first restaurant you visit.) (a) What is the probability that you have to visit four restaurants to find the first one that has chicken? (2 points) (b) What is the probability that you have to try more than two restaurants? (2 points) (c) What is the expected number of restaurants that you must visit? The variance? (2 points)