{ "__type": "IngestedDoc", "__tag": 4010, "_content": { "Notes": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The probability mass function (PMF) for the Hypergeometric distribution is" } ] }, { "__type": "Math", "__tag": 4058, "value": "P(x) = \\frac{\\binom{g}{x}\\binom{b}{n-x}}{\\binom{g+b}{n}}," }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "where " }, { "__type": "InlineMath", "__tag": 4057, "value": "0 \\le x \\le n" }, { "__type": "Text", "__tag": 4046, "value": " and " }, { "__type": "InlineMath", "__tag": 4057, "value": "n-b \\le x \\le g" } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "for P(x) the probability of " }, { "__type": "InlineCode", "__tag": 4051, "value": "x" }, { "__type": "Text", "__tag": 4046, "value": " good results in the drawn sample, g = " }, { "__type": "ParamRef", "__tag": 4071, "name": "ngood" }, { "__type": "Text", "__tag": 4046, "value": ", b = " }, { "__type": "ParamRef", "__tag": 4071, "name": "nbad" }, { "__type": "Text", "__tag": 4046, "value": ", and n = " }, { "__type": "ParamRef", "__tag": 4071, "name": "nsample" }, { "__type": "Text", "__tag": 4046, "value": "." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Consider an urn with black and white marbles in it, " }, { "__type": "ParamRef", "__tag": 4071, "name": "ngood" }, { "__type": "Text", "__tag": 4046, "value": " of them are black and " }, { "__type": "ParamRef", "__tag": 4071, "name": "nbad" }, { "__type": "Text", "__tag": 4046, "value": " are white. 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[1] Lentner, Marvin, \"Elementary Applied Statistics\", Bogden", " and Quigley, 1972.", ".. [2] Weisstein, Eric W. \"Hypergeometric Distribution.\" From", " MathWorld--A Wolfram Web Resource.", " https://mathworld.wolfram.com/HypergeometricDistribution.html", ".. [3] Wikipedia, \"Hypergeometric distribution\",", " https://en.wikipedia.org/wiki/Hypergeometric_distribution" ], "qa": "numpy.random:RandomState.hypergeometric", "arbitrary": [], "local_refs": [ "nbad", "ngood", "nsample", "out", "size" ] }