A random sample of size $n$ is taken from a gamma distribution with parameters $α = 8 $and $λ = 1/θ$. The sample mean is $\bar{x}$ and $θ$ is to be estimated.
Determine the mean square error of the MME of $θ$.
My attempt,
$$E(X)=\frac{8}{\frac{1}{\theta}}$$ $$\hat{\theta}{=\frac{\bar{x}}{8}}$$
$$Bias(\theta)=E(\hat{\theta})-\theta=0$$
$$MSE=Var(\frac{\bar{x}}{8})$$
Can I know how to proceed for it? Thanks in advance