Exercise 1.  Three balls are randomly chosen with replacement from an urn containing 2 blue, 3 red, and 2 yellow balls. Let denote the number of red balls chosen.

1. What are the possible values of ?
2. What is the density function of ?

Exercise 2.  We throw two dice. Let be the sum.

1. Compute .
2. Compute

Honors exercise.

An insurance company fi􏰃nds that Mark has a 7% chance of getting into a car accident in the next year. If Mark has any kind of accident then the company guarantees to pay him $10, 000. The company has decided to charge Mark a $180 premium for this one year insurance policy.
(a) Let X be the amount proof􏰃t or loss from this insurance policy in the next year for the insurance company. Find E(X), the expected return for the Insurance company? Should the insurance company charge more or less on its premium?
(b) What amount should the insurance company charge Mark in order to guarantee an expected return of $100?