You are playing a game where you roll a die and win 0 jellyb

You are playing a game where you roll a die and win 0 jellybeans for rolling a one or two; 1 jellybean for rolling a three, four, or five; and 2 jellybeans for rolling a six. Each time you play the game, you must pay 1 jellybean.

(a) What is the expected number of jellybeans you win each round?

(b) What is the variance of the number of jellybeans that you win?

(c) If you like jellybeans, is this a game you want to play?

please show how the equation is used and how you solve for solutions

Solution

You are playing a game where you roll a die and win 0 jellybeans for rolling a 1, 2, or 3; 1 jellybean for rolling a 4, or 5; and 3 jellybeans for rolling a 6.

Each time you play the game, you must pay 1 jellybean.

x (wins - paid)

rolls

Probability

x*p(x)

x^2*p(x)

-1

1, 2, 3

1/2

- 1/2

1/2

0

4, 5,

1/3

0   

0   

2

6

1/6

1/3

2/3

sum:

- 1/6

1 1/6

(a) What is the expected number of jellybeans you win each round (including the one you pay)?

From last line: Expected number = -1/6 or -.1667

(b) What is the variance of the number of jellybeans that you win?

From last line: Variance = 1 1/6