For the past 18 months, Glenda has been admiring the Pacita Abad artworks, made out of handmade paper, on display at the school. So the course description corresponds with Glenda's expectations of an overseas exchange experience. On this exchange, she also asked her classmate John to join her. (1) The exchange will be at a university in the city of Kyoto, Japan. To fund the overseas trip, Glenda and John need to set up a booth to raise money. They plan to sell letter stationery made from washi. They set up a booth on campus. Let N be the number of visitors in an hour. They estimate that on average 15 people would visit the booth every hour with a probability of p = 0.2 that a visitor would purchase a set. Let Y be the number of sets they could sell in an hour, assuming the booth is open for 6 hours a day and that every visitor acts independently of others. (a) Find a suitable distribution for N. State all assumptions. (b) Are N and Y related? Write down expressions for the joint PDF of N and Y, and marginal PDF of Y (c) Find a suitable distribution for Y and then combine with (a) and (b) to write downan expression for P(Y = k). Do not evaluate this expression. (d) Find E(Y) and var(Y). (e) Write an expression for P(Y ≥ k), and comment. (f) Let W be the total number of sets sold in 10 days, sketch the distribution of W and comment on the shape of the distribution (f) Let W be the total number of sets sold in 10 days, sketch the distribution of W and comment on the shape of the distribution. (g) Based on (f), find an approximation of P(W > 576). Compare this to (e) and comment.