The distribution of grades in an easy introductory statistics course is as follows: Grade A B C D F Probability 0.4 0.3 0.2 0.1 0.0 Find the expected value. This is the average grade in this course....

The distribution of grades in an easy introductory statistics course is as follows:

1. Find the expected value. This is the average grade in this course.


2. 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 part (a). (The law of large numbers says that the estimate will be very accurate if we simulate a very large number of students.