ProbabilityDistribution

ProbabilityDistribution[pdf, {x, xmin, xmax}] represents the continuous distribution with PDF pdf in the variable x where the pdf is taken to be zero for x < xmin and x > xmax.

ProbabilityDistribution[pdf, {x, xmin, xmax, 1}] represents the discrete distribution with PDF pdf in the variable x where the pdf is taken to be zero for x < xmin and x > xmax.

ProbabilityDistribution[pdf, {x, ...}, {y, ...}, ...] represents a multivariate distribution with PDF pdf in the variables x, y, ..., etc.

ProbabilityDistribution[{"CDF", cdf}, ...] represents a probability distribution with CDF given by cdf.

ProbabilityDistribution[{"SF", sf}, ...] represents a probability distribution with survival function given by sf.

ProbabilityDistribution[{"HF", hf}, ...] represents a probability distribution with hazard function given by hf.

Examples

dist = ProbabilityDistribution[2 x, {x, 0, 1}]
Mean[dist]

Please visit the official Wolfram Language Reference for more details.