Let $D(\mu, \Sigma)$ represent an arbitrary distribution with mean $\mu$ and covariance $\Sigma$.
I am given that $\beta_k$ is a vector of length $M_k$: $$\beta_k \sim D\left(0, \frac{\sigma^2_k}{M_k} I_{M_k} \right)$$ where I am given the value $\sigma^2_k$.
What exactly does this mean? Are we saying that the covariance of the $M_k$ elements in $\beta_k$ is is given by $\frac{\sigma^2_k}{M_k}$? In that case, where would the matrix $I_{M_k}$ come into play? This doesn't really seem like a distribution then?
Thanks in advance for any help!