Suppose that $X_1,X_2,\ldots,X_n$ form a random sample from a Normal distribution with unknown mean $\mu$ and known variance $\sigma^2$, and the prior distribution of $\mu$ is a normal distribution with mean 0 and variance $\sigma^2$.

(a) Obtain the posterior distribution for $\sigma^2$.

(b) Show that if n is large then the posterior distribution of mu given that $X_i = x_i$, $(i = 1; ... ; n)$ will be approximately a normal distribution with mean $x_n$ and variance $\sigma^2/n$.

Edit: I believe this question has to do with conjugate priors so feel free to steer me in the right direction if this is incorrect! Thanks beforehand.