1. ## Estimation

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

2. 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.

3. Consider parameters $\displaystyle k, \theta$ such that $\displaystyle \mu = k\theta$ and $\displaystyle \sigma^2 =k\theta^2$

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

The pdf will then be $\displaystyle P(x) =\frac{x^{k-1}e^{\frac{-x}{\theta}}}{\Gamma (k)\theta^k}$

4. is that really all there is to it?