The support of a probability distribution is the set of outcomes that can occur. For a discrete distribution, it may be finite—such as 1 through 6 for a die—or infinite, such as the positive integers. A probability mass function assigns a probability to each member of the support; sampling returns one of those outcomes according to those probabilities. section 12.2
Support provides the domain that distribution operations work over:
- Uniform sampling uses the support 0 through n−1; Random.Next(6) therefore samples six possible integers. section 12.3
- A discrete distribution can enumerate its support, sample from it, and report each outcome’s weight. section 12.4
- Projecting outcomes can merge several input values into one output, so the projected support may be smaller while its weights are summed. section 12.7
- An empty distribution has no support: every outcome is impossible and every weight is zero. section 14.2
A colored die
Map a six-sided fair die to [green, blue, red, blue, red, blue]. The input support has six values, but the output support is {green, blue, red}; grouping inputs gives weights 1, 3, and 2. section 12.7
var rnd = new Random();
int roll = rnd.Next(6);
A minimal C# example makes the support of a uniform distribution visible: Random.Next(6) can return exactly the integers 0 through 5. section 12.3
