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Suppose A and B are two random variables and given by $A = s\delta_1$ and $B = s\delta_2$, where $\delta_1$ and $\delta_2$ are fixed and known, however $s \sim N(0,1)$.

What does the joint distribution of $p(A,B)$ look like ?

In general, what is $p(A,A)$ ?

It seems to be that the joint is only dictated by $s$ which is the only random number in this case, and therefore the joint $p(A,B)$ can be equivalently written as $p(s)$, however I'm not a mathematician hence I'm not sure about the exact math. Thanks!

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