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I want the PMF and cumulative probabilities for every k."},{"title":"Hypergeometric sampling from a batch","prompt":"We have a population of N=200 parts, K=30 of which are defective, and we're drawing n=15 at random. Give me the full hypergeometric probability table including P(X<=k) and P(X>=k) for each outcome."}],"resultDescription":"Returns a JSON object containing the distribution's mean, mode, variance, support range, and a table array where each row has k (outcome value), probability (PMF), cumulative (CDF), and upperTail (P(X>=k)). 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