| 30,000 | 0.05 | 1,500 | |
| 2 | 15,000 | 0.20 | 3,000 |
| 3 | 10,000 | 0.45 | 4,500 |
| 4 | 7,500 | 0.30 | 2,250 |
| Sum | 11,250 |
If you find a winning ticket in your package, you win—on average— E($30,000/W) = $11,250). The expected value of the amount won is probably larger than you anticipated. We expect E(W) = 3 winners to share the prize, but the expected value E(30,000/W) is larger than 30,000/E(W) = 30,000/3 = $10,000.
What Do You Think?
People who play the carnival game Lucky Ducks pick a plastic duck from among those floating in a small pool. Each duck has a value written on the bottom that determines the prize. Most say “Sorry, try again!” Otherwise, 25% pay $1, 15% pay $5, and 5% pay $20. Let the random variable Y denote the winnings from picking a duck at random. ...
Get Statistics for Business: Decision Making and Analysis, 3rd Edition now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.
