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Suppose that y1,...,yn|β are iid Exponential with mean 1/β and that β is marginally Exponential with...

Suppose that y1,...,yn|β are iid Exponential with mean 1/β and that β is marginally Exponential with mean 1. Show that β|y1,...,yn follows a Gamma distribution with shape parameter n+1 and rate parameter 1+∑yi.

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