1) Suppose that a school has 20 classes: 16 with 25 students in each, three with 100 students in each, and one with 300 students, for a total of 1000 students.

a) What is the average class size?

b) Select a student randomly out of the 1000 students. Let the random variable X equal the size of the class to which this student belongs, and define the p.m.f. of X.

c) Find E(X), the expected value of X. Does this answer surprise you?

2) In the casino game called high-low, there are three possible bets. Assume that $1, is the size of the bet. A pair of six-sided dice is rolled and their sum is calculated. If you bet low, you win $1 if the sum of the dice is {2,3,4,5,6}. If you bet high, you win $1 if the sum of the dice is {8,9,10,11,12}. If you bet on {7}, you win $4 if a sum of 7 is rolled. Otherwise you lose on each of the three bets. In all three cases, your original dollar is returned if you win. Find the expected value of the game to the bettor for each of these three bets.

a) What is the average class size?

b) Select a student randomly out of the 1000 students. Let the random variable X equal the size of the class to which this student belongs, and define the p.m.f. of X.

c) Find E(X), the expected value of X. Does this answer surprise you?

2) In the casino game called high-low, there are three possible bets. Assume that $1, is the size of the bet. A pair of six-sided dice is rolled and their sum is calculated. If you bet low, you win $1 if the sum of the dice is {2,3,4,5,6}. If you bet high, you win $1 if the sum of the dice is {8,9,10,11,12}. If you bet on {7}, you win $4 if a sum of 7 is rolled. Otherwise you lose on each of the three bets. In all three cases, your original dollar is returned if you win. Find the expected value of the game to the bettor for each of these three bets.