Replacement from an urn of random composition

Reference no: EM131833076

The probability law of the number of white balls in a sample drawn without replacement from an urn of random composition. Consider an urn containing N balls. Suppose that the number of white balls in the urn is a numerical valued random phenomenon obeying (i) a binomial probability law with parameters N and p, (ii) a hyper geometric probability law with parameters M, N, and p. [For example, suppose that the balls in the urn constitute a sample of size N drawn with replacement (without replacement) from a box containing M balls, of which a proportion p is white.] Let a sample of size n be drawn without replacement from the urn. Show that the number of white balls in the sample obeys either a binomial probability law with parameters n and p, or a hyper geometric probability law with parameters M, n, and p, depending on whether the number of white balls in the urn obeys a binomial or a hyper geometric probability law.

Reference no: EM131833076

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