What is this distribution formulated with w, m and sum sign?

Question

I have a binary classification problem, part of which is defined as follows :

p(x|y=1) $\sim w (m_1 , \sum_1$)

and

p(x|y=0) $\sim w (m_0 , \sum_0$)

Where $\sum_1$ is a covariance matrix :

$$ \begin{bmatrix} \sigma^2 & 0\\ 0 & \sigma^2 \\ \end{bmatrix} $$

So what is this distribution?

Note : I am supposed to find a generative model for classification.

Thanks for any help!

Answer 1

After reviewing the lecture notes , it turns out this is a normal distribution around mean $m_1$ and variance $\sigma$. The different notation is because the means are vectors instead of scalars. The dimension of m is equal to the dimension of the covariance matrix.