Melody Green is a surgeon at Green-Stone Memorial hospital. On any given day there is a 60% chance she will have to perform at least one emergency surgery. She also has a 30% chance of having a coworker buying her a coffee. Suppose that these two events are independent and that days are independent. (a) Let Y be the random variable that indicates whether Melody has an emergency surgery on a given day. What is the PMF of Y ? (b) Let X be the random variable that indicates whether a coworker buying Melody a coffee on a given day. What is the PMF of X? (c) Let Z = X + Y . What is the interpretation of Z = 1 in the context of the problem? (d) What is P(Z = 1)?