Concept explainers
(a)
To find: The average of the payoff distribution for the provided bets.
(a)
Answer to Problem 139E
Solution: The average of the payoff distribution for the provided bets is
Explanation of Solution
Calculation: When the point 4 is obtained, then the probability of winning the bet is
Value of X | 1 | 0 |
Probability |
The mean of the distribution can be calculated as:
When the point 5 or 9 is obtained, then the probability of winning is
Value of X | 1 | 0 |
Probability |
The mean of the distribution can be calculated as:
When the point 5 or 9 is obtained, then the probability of winning is
Value of X | 1 | 0 |
Probability |
The mean of the distribution can be calculated as:
When the point 6 or 8 is obtained, then the probability of winning is
Value of X | 1 | 0 |
Probability |
The mean of the distribution can be calculated as:
(b)
To test: Whether the bets are fair and the average of the distribution of the payoff is 0.
(b)
Answer to Problem 139E
Solution: Yes, the bets are fair and the average of the distribution of the payoff is 0.
Explanation of Solution
Calculation: When betting $10 on any point, if bet is won by the individual he would receive $20, if the bet is lost by him then he would lost $10. Thus, the difference between bet amount and the average of the distribution of the payoff can be calculated as:
The difference between bet amount and the average of the distribution of the payoff is obtained 0.
When the point5 or 9 is obtained, then the probability of winning is
Value of X | 1 | 0 |
Probability |
The mean of the distribution can be calculated as:
When betting $10 on any point, if bet is won by the individual he would receive $15, if the bet is lost by him then he would lost $10. Thus, the difference between bet amount and the average of the distribution of the payoff can be calculated as:
The difference between bet amount and the average of the distribution of the payoff is obtained 0.
When the point 6 or 8 is obtained, then the probability of winning is
Value of X | 1 | 0 |
Probability |
The mean of the distribution can be calculated as:
When betting $10 on any point, if bet is won by the individual he would receive $12, if the bet is lost by him then he would lost $10. Thus, the difference between bet amount and the average of the distribution of the payoff can be calculated as:
The difference between bet amount and the average of the distribution of the payoff is obtained 0.
Conclusion: The difference between bet amount and the average of the distribution of the payoff is obtained as zero, if the difference were not 0 then the bet would not be considered as fair bet.
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Chapter 4 Solutions
LaunchPad for Moore's Introduction to the Practice of Statistics (12 month access)