Introduction to the Practice of Statistics: w/CrunchIt/EESEE Access Card
8th Edition
ISBN: 9781464158933
Author: David S. Moore, George P. McCabe, Bruce A. Craig
Publisher: W. H. Freeman
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Chapter 4, Problem 139E
(a)
To determine
To find: The average of the payoff distribution for the provided bets.
(a)
Expert Solution
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
| Value of X | 1 | 0 |
| Probability |
The
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 determine
To test: Whether the bets are fair and the average of the distribution of the payoff is 0.
(b)
Expert Solution
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
Introduction to the Practice of Statistics: w/CrunchIt/EESEE Access Card
Ch. 4.1 - Prob. 1UYKCh. 4.1 - Prob. 2ECh. 4.1 - Prob. 3ECh. 4.1 - Prob. 4ECh. 4.1 - Prob. 5ECh. 4.1 - Prob. 6ECh. 4.1 - Prob. 7ECh. 4.1 - Prob. 8ECh. 4.1 - Prob. 9ECh. 4.2 - Prob. 10UYK
Ch. 4.2 - Prob. 11UYKCh. 4.2 - Prob. 12UYKCh. 4.2 - Prob. 13UYKCh. 4.2 - Prob. 14UYKCh. 4.2 - Prob. 15UYKCh. 4.2 - Prob. 16UYKCh. 4.2 - Prob. 17UYKCh. 4.2 - Prob. 18UYKCh. 4.2 - Prob. 19ECh. 4.2 - Prob. 20ECh. 4.2 - Prob. 21ECh. 4.2 - Prob. 22ECh. 4.2 - Prob. 23ECh. 4.2 - Prob. 24ECh. 4.2 - Prob. 25ECh. 4.2 - Prob. 26ECh. 4.2 - Prob. 27ECh. 4.2 - Prob. 28ECh. 4.2 - Prob. 29ECh. 4.2 - Prob. 30ECh. 4.2 - Prob. 31ECh. 4.2 - Prob. 32ECh. 4.2 - Prob. 33ECh. 4.2 - Prob. 34ECh. 4.2 - Prob. 35ECh. 4.2 - Prob. 36ECh. 4.2 - Prob. 37ECh. 4.2 - Prob. 38ECh. 4.2 - Prob. 39ECh. 4.2 - Prob. 40ECh. 4.2 - Prob. 41ECh. 4.2 - Prob. 42ECh. 4.2 - Prob. 43ECh. 4.2 - Prob. 44ECh. 4.2 - Prob. 45ECh. 4.3 - Prob. 46UYKCh. 4.3 - Prob. 47UYKCh. 4.3 - Prob. 48UYKCh. 4.3 - Prob. 49ECh. 4.3 - Prob. 50ECh. 4.3 - Prob. 51ECh. 4.3 - Prob. 52ECh. 4.3 - Prob. 53ECh. 4.3 - Prob. 54ECh. 4.3 - Prob. 55ECh. 4.3 - Prob. 56ECh. 4.3 - Prob. 57ECh. 4.3 - Prob. 58ECh. 4.3 - Prob. 59ECh. 4.3 - Prob. 60ECh. 4.3 - Prob. 61ECh. 4.3 - Prob. 62ECh. 4.3 - Prob. 63ECh. 4.3 - Prob. 64ECh. 4.3 - Prob. 65ECh. 4.3 - Prob. 66ECh. 4.4 - Prob. 66UYKCh. 4.4 - Prob. 67UYKCh. 4.4 - Prob. 68UYKCh. 4.4 - Prob. 69UYKCh. 4.4 - Prob. 70UYKCh. 4.4 - Prob. 71UYKCh. 4.4 - Prob. 72ECh. 4.4 - Prob. 73ECh. 4.4 - Prob. 74ECh. 4.4 - Prob. 75ECh. 4.4 - Prob. 76ECh. 4.4 - Prob. 77ECh. 4.4 - Prob. 78ECh. 4.4 - Prob. 79ECh. 4.4 - Prob. 80ECh. 4.4 - Prob. 81ECh. 4.4 - Prob. 82ECh. 4.4 - Prob. 83ECh. 4.4 - Prob. 84ECh. 4.4 - Prob. 85ECh. 4.4 - Prob. 86ECh. 4.4 - Prob. 87ECh. 4.4 - Prob. 88ECh. 4.4 - Prob. 89ECh. 4.4 - Prob. 90ECh. 4.4 - Prob. 91ECh. 4.4 - Prob. 92ECh. 4.4 - Prob. 93ECh. 4.4 - Prob. 94ECh. 4.5 - Prob. 95UYKCh. 4.5 - Prob. 96UYKCh. 4.5 - Prob. 97UYKCh. 4.5 - Prob. 98UYKCh. 4.5 - Prob. 99UYKCh. 4.5 - Prob. 100UYKCh. 4.5 - Prob. 101UYKCh. 4.5 - Prob. 102ECh. 4.5 - Prob. 103ECh. 4.5 - Prob. 104ECh. 4.5 - Prob. 105ECh. 4.5 - Prob. 106ECh. 4.5 - Prob. 107ECh. 4.5 - Prob. 108ECh. 4.5 - Prob. 109ECh. 4.5 - Prob. 110ECh. 4.5 - Prob. 111ECh. 4.5 - Prob. 112ECh. 4.5 - Prob. 113ECh. 4.5 - Prob. 114ECh. 4.5 - Prob. 115ECh. 4.5 - Prob. 116ECh. 4.5 - Prob. 117ECh. 4.5 - Prob. 118ECh. 4.5 - Prob. 119ECh. 4.5 - Prob. 120ECh. 4.5 - Prob. 121ECh. 4.5 - Prob. 122ECh. 4.5 - Prob. 123ECh. 4.5 - Prob. 124ECh. 4.5 - Prob. 125ECh. 4.5 - Prob. 126ECh. 4.5 - Prob. 127ECh. 4.5 - Prob. 128ECh. 4.5 - Prob. 129ECh. 4.5 - Prob. 130ECh. 4.5 - Prob. 131ECh. 4 - Prob. 132ECh. 4 - Prob. 133ECh. 4 - Prob. 134ECh. 4 - Prob. 135ECh. 4 - Prob. 136ECh. 4 - Prob. 137ECh. 4 - Prob. 138ECh. 4 - Prob. 139ECh. 4 - Prob. 140ECh. 4 - Prob. 141ECh. 4 - Prob. 142ECh. 4 - Prob. 143ECh. 4 - Prob. 144ECh. 4 - Prob. 145ECh. 4 - Prob. 146ECh. 4 - Prob. 147ECh. 4 - Prob. 148ECh. 4 - Prob. 149ECh. 4 - Prob. 150ECh. 4 - Prob. 151ECh. 4 - Prob. 152E
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