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. What is the expected number of jellybeans you win each round? What is the variance of the number of jellybeans that you win? If you like jellybeans, is this a game you want to play?

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

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