Exercise 1 (Each part 1 mark). Consider a class of 50 students. For each student, a fair six-sided die will be rolled to determine the students final grade. If the die shows 6, the grade is 90. If the die shows any other number, the grade is 40. Let Xi be the grade of the i-th student. Let Z = 1 50 P50 i=1 Xi be the class average. (a) What is the expected grade of the i-th student? (b) If only 8 students roll a 6, what is the class average? (c) What is the expected class average?