# Mathematics - Probability distribution function

The probability distribution function is used to specify relative likelihood of different outcomes of a single experiment.

It assigns a probability (a nonnegative number) to each possible outcome.

The probabilities of all the possible outcomes must sum to 1.

## 3 - Uniform distribution

Often the probability distribution is a uniform distribution. It assigns the same probability to each outcome.

To model rolling a die, the possible outcomes are 1, 2, 3, 4, 5, and 6, and the probabilities are

Pr(1) = Pr(2) = Pr(3) = Pr(4) = Pr(5) = Pr(6) = 1/6

In Python:

Pr = {1:1/6, 2:1/6, 3:1/6, 4:1/6, 5:1/6, 6:1/6}

To model the flipping of two coins, the possible outcomes are HH, HT, TH, TT and the probability of all outcomes is 1/4. In Python,

Pr = {('H', 'H'):1/4, ('H', 'T'):1/4, ('T', 'H'):1/4, ('T', 'T'):1/4}