Course grades. The distribution of grades in a large statistics course is as follows:

Grade: A B C D F Probability: 0.2 0.3 0.3 0.1 0.1 To calculate student grade point averages, grades are expressed in a numerical scale with A = 4, B = 3, and so on down to F = 0.

(a) Find the expected value. This is the average grade in this course.

(b) Explain how to simulate choosing students at random and recording their grades. Simulate 50 students and find the mean of their 50 grades. Compare this estimate of the expected value with the exact expected value from (a). (The law of large numbers says that the estimate will be very accurate if we simulate a very large number of students.)