Discrete & Continuous Random Variables - Statistics

Hypergeometric DistributionIn spite of its hyper name, this distribution is modeled by a very simple urn model.We randomly grab k balls from an urn containing m red balls and n black balls.The term grab is used to emphasize selection without replacement.Let X denote the number of red balls that are selected in this grab.X is a hypergeometric random variable with a hypergeometric distribution.If we observe X = x we grabbed x red balls and k − x black balls from the urn.The following restrictions apply: 0 ≤ x ≤ min(m,k) and0 ≤ k − x ≤ min(n,k)i.e., k − min(n,k) ≤ x ≤ min(m,k) or max(0,k − n) ≤ x ≤ min(m,k)X(S) = {x ∈ Z : max(0,k − n) ≤ x ≤ min(m,k)}7