Suppose that a random sample of sizen is taken from a Poisson distribution for which the value of the mean e is unknown, and the prior distribution of e is a gamma distribution for which the mean is...

Extracted text: Suppose that a random sample of sizen is taken from a Poisson distribution for which the value of the mean e is unknown, and the prior distribution of e is a gamma distribution for which the mean is Po. Show that the mean of the posterior distribution of e will be a weighted average having the form Y,X, + (1– Yn)Ho, and show that yn →1 as n- *.