Definition
Probability Distribution
A probability distribution, also called a law, is a probability measure on a measurable space of possible values
. Let
be a random variable on a probability space . The distribution of is the measure Thus
assigns probabilities to sets of underlying outcomes, while assigns probabilities to sets of values of . A distribution is not a different kind of measure: it is a probability measure viewed as a law of values. The notation
means that has distribution , that is, .