Card game. Consider the following card game with a well-shuffled deck of cards. If you draw a red card, you win nothing. If you get a spade, you win $5. For any club, you win $10 plus an extra $20 for the ace of clubs.
Create a probability model for the amount you win at this game. Also, find the expected winnings for a single game and the standard deviation of the winnings.
What is the maximum amount you would be willing to pay to play this game? Explain.
knitr::kable(random_variables)| X | PX |
|---|---|
| 0 | 0.5000000 |
| 5 | 0.2500000 |
| 10 | 0.2500000 |
| 30 | 0.0192308 |
expectedWin_X <- round(sum(random_variables$X * random_variables$PX),2);## [1] "The expected win for the above distribution is 4.33"variance_X <- round(sum(random_variables$PX *(random_variables$X - expectedWin_X)^2),2);## [1] "The variance of win for the above distribution is 30.20"standardDeviation_X <- round(sqrt(variance_X),2);## [1] "The standard deviation of win for the above distribution is 5.50"