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Let X be N(O, 1/0). Assume that the unknown O is a value of a random variable 0 which has a gamma distribution with parameters IX = r/2 and fJ = 2/r, where r is a positive integer. Show that X has a marginal I-distribution with r degrees of freedom. This procedure is called compounding, and it may be used by a Bayesian statistician as a way of first presenting the I-distribution, as well as other distributions.

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Category:- Statistics and Probability
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