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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.

Please visit the official Wolfram Language Reference for more details and examples on core symbols.