Consider the following game. You roll a fair die. If you roll a 5 or 6 you select a ball from Jar 2.

Otherwise, you select a ball from Jar 1. Jar 1 contains 15 red balls and 5 green balls while Jar 2 contains

8 red balls and 12 green balls. You are given $1 if you roll a 5 or 6 and $3 if you roll a 1 through 4. Let the random variable X represent your profit from the die part of the game. If you select a red ball, you are given $4. If you select a green ball, you are given $2. Let the random variable Y represent the profit from the ball selection part of the game. Let Z = X + Y.

You will play the game once.

Problem 5. Find E(Z) and the standard deviation

Problem 6. Find E(XY).

Problem 7. Find the correlation of X and Y