When the value of a certain variable `X` depends on chance, you call `X` a stochastic variable. You can calculate the corresponding probability of every value of `X` (using a probability tree). All probabilities together form the probability distribution of `X` . The probability distribution is often given as a table.
When you are throwing with two dice and call the number of sixes `X` , then `X` is an example of a probability distribution. You can calculate the corresponding probability distribution using the probability tree.
x | 0 | 1 | 2 |
Ρ(X=x) | 25/36 | 10/36 | 1/36 |
Check that the sum of all probabilities in such a probability density equals 1.
On average when throwing two dice the number of times that you get two sixes is .
This number is called the expected value of the number of sixes when throwing two dice: in one of every three throws (with
two dice) a six comes up... when throwing often enough.