How do you construct a probability distribution?

Answer 1

First decide whether the event space is discrete or continuous.

For a discrete event space, for each outcome in the space assign a probability: a number in the interval [0, 1] such that the sum of probabilities for all outcomes is 1. The mapping from the event space to the probabilities is the probability distribution function.

The procedure for a continuous event space is analogous: the sum is replaced by the integral.