Ann has been asked to help with an important event taking place at the GT Stadium. Three different classes of sponsors will be invited to a football game. There are 20 sponsors in Class A, 30 sponsors in Class B, and 10 sponsors in Class C. The GT Team will be playing against the OSU on the day of the event, which means the tickets will be certainly sold out. Thus, Ann should commit to the number of tickets he needs at least 2 months before the football season starts. Working with GT administration, Ann has come up with the goal of committing to the minimum number of tickets such thatthere is a 90% chance or more that all invited sponsors who attend have a seat.

Suppose that X,- is a random variable representing whether or not the trim individual shows up to the event. Specically. X- = 0 if sponsor i does not show up to the event, ' 1 if sponsor '3' shows up to the event. Moreover, let P(X, = 1} = p and PUL- = D) = 1 p. Forthe following questions, assume that each sponsor makes an attendance decision independently. In math, this is typically expressed as X,- J.L X j, W 3E j. As a result, X1- is assumed to be independent and identically distributed (Lid). Questions 1. Characterize the probability distribution function for the random variable Y 2 X1 + X2. In other words, compute P[Y = y) for every possible value 3; that Y might end up being. 2. Let N be the uncertain number of sponsors who show up to the event. Hovur would you express N in terms of X35? 3. What is the probability distribution function for N