x 2 right-parenthesis"/>, a loss of 11 is incurred twice, with throws of (5,6) and (6,5).
Accordingly, let the sample space for the wager be
let the measurable sets
Table 2.1 Distribution of payouts.
| Payout | Probability |
|---|---|
| 1 |
|
| 2 |
|
| 3 |
|
| 4 |
|
| 5 |
|
| ‐11 |
|
| ‐12 |
|
Now define random variable
or slightly more than 1 euro.
The random variables
Measurability ensures that the two forms are related. To illustrate, consider
which is a subset
This kind of relationship is generally valid for contingent and elementary forms of random variables.
2.2 Probability and Riemann Sums
Elementary statistical calculation is often learned by performing exercises such as the following.
Example 4
