Let's say I have two (normal) random variables $A1$ and $A2$ and during a random process, at each time instant, I am collecting a sample for each one of them.
Given the samples I collected, I can calculate two normal distributions to describe $A1$ and $A2$, respectively $\mathcal{N}(\mu_1, \sigma_1)$ and $\mathcal{N}(\mu_2, \sigma_2)$.
I want to know, given my estimated Gaussians and the samples I collected, how to calculate the joint probability distribution of the random vector $(A1, A2)$.