I would like to find out if it is possible to calculate the distribution parameters, i.e., determine $\mu$, $\sigma$, for a random variable $y$, given that:
\begin{align} y &\backsim Normal(\mu, \sigma) \\ \mu &\backsim Normal(a, b) \\ \sigma &\backsim Normal(n, m) \end{align}
where $a,b,n,m$ are known distribution parameters.
I have been able to model the system using a very simple Monte Carlo simulation method which I used to estimate the the parameters, however I would like to check my results using an analytical method.