suppose that the prior distribution of some parameter theta is a gamma distribution for which the mean is 10 and the variance is 5. determine the prior pdf of theta

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- Feb 3rd 2011, 06:46 PMholly123Estimation
suppose that the prior distribution of some parameter theta is a gamma distribution for which the mean is 10 and the variance is 5. determine the prior pdf of theta

- Feb 3rd 2011, 06:55 PMtheodds
Unless there is something I'm missing, there doesn't seem to be a question here. They tell you the distribution of theta. You know the mean and variance of a gamma; solve for the usual parameters.

- Feb 3rd 2011, 06:57 PMpickslides
Consider parameters $\displaystyle \displaystyle k, \theta $ such that $\displaystyle \displaystyle \mu = k\theta $ and $\displaystyle \displaystyle \sigma^2 =k\theta^2$

You are told $\displaystyle \displaystyle k\theta =10 , k\theta^2 = 5$ solve for $\displaystyle \displaystyle k, \theta$

The pdf will then be $\displaystyle \displaystyle P(x) =\frac{x^{k-1}e^{\frac{-x}{\theta}}}{\Gamma (k)\theta^k}$ - Feb 3rd 2011, 06:57 PMholly123
is that really all there is to it?

- Feb 3rd 2011, 07:07 PMpickslides
That's what I read.

The whole 'prior' thing made it sounds bigger than what it was. But everything described was prior so it all links together easily.