Problem 6. Your section in the probability course you are attending consists of 5 students and meets for a total of 11 times. Each session ends with a short quiz. The score of each of the 5 students is equally likely to be 1,2,3, or 4, independently of other students. Let ) be the sum of the quiz scores of the students in today's session. (a) Find the mgf of Q. (b) Find the range of @ and calculate P(Q = q) for = 6,10, 12,15, 18. 2 (c) Suppose that the time to grade all of the quizzes from a single session is a normal random variable with mean 30 minutes and variance 5 minutes, independently of other sessions. Find the PDF and mgf associated with the total amount of time spend to grade the quizzes for all 11 sessions