Probability > Probability distribution
1234Probability distribution

Theory

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 0 25 36 + 1 10 36 + 2 1 36 = 12 36 = 1 3 .
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.

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