Homework SourseA game is played by tossing a coin and rolling a die There a
A game is played by tossing a coin and rolling a die. There are 12 possible equally likely outcomes. If the coin is T\'s you win the number on the die in dollars. If the Coin is H\'s, you win twice the number on the die in dollars. The random varible X gives the amount of your winnings.
Possible outcomes
winnings
T1
1
T2
2
T3
3
T4
4
T5
5
T6
6
T7
2
T8
4
T9
6
T10
8
T11
10
T12
12
This is the table I came up with.
A.) List all the possible amounts you could win.
B.) How much would you be willing to pay for this game
C.) Find the Variance and Standard Deviation of your winnings?
| Possible outcomes | winnings |
| T1 | 1 |
| T2 | 2 |
| T3 | 3 |
| T4 | 4 |
| T5 | 5 |
| T6 | 6 |
| T7 | 2 |
| T8 | 4 |
| T9 | 6 |
| T10 | 8 |
| T11 | 10 |
| T12 | 12 |
Solution
As expected win is 5 1/4 dollars, we can pay upto 5 1/4 dollars.
Variance of winnings =E(Gain^2) - Mean gain^2
= 37 11/12 - 21^2/16
= 37.917-27.562
= 10.355
Std dev = 3.218
| Possible outcomes | winnings | Prob for 1 | Prob for T/H | Prob T1 | Expected gain |
| T1 | 1 | 1/6 | 1/2 | 1/12 | 1/12 |
| T2 | 2 | 1/6 | 1/2 | 1/12 | 1/6 |
| T3 | 3 | 1/6 | 1/2 | 1/12 | 1/4 |
| T4 | 4 | 1/6 | 1/2 | 1/12 | 1/3 |
| T5 | 5 | 1/6 | 1/2 | 1/12 | 5/12 |
| T6 | 6 | 1/6 | 1/2 | 1/12 | 1/2 |
| T7 | 2 | 1/6 | 1/2 | 1/12 | 1/6 |
| T8 | 4 | 1/6 | 1/2 | 1/12 | 1/3 |
| T9 | 6 | 1/6 | 1/2 | 1/12 | 1/2 |
| T10 | 8 | 1/6 | 1/2 | 1/12 | 2/3 |
| T11 | 10 | 1/6 | 1/2 | 1/12 | 5/6 |
| T12 | 12 | 1/6 | 1/2 | 1/12 | 1 |
| Total | 5 1/4 |
