So it’s been a while since I’ve updated this blog. The short (and complete) story is that I’ve been rushing final projects for school. There might be a new article on that (later)
Now that I am reviewing some of my SOCMLx notes (still need to scribe some stuff up), I want to revisit a topic that has always troubled me. Specifically:
$$ E[X] vs E[XY] $$
In both of these expectations, what does the expectation refer to?
It turns out that just having the $$E$$ symbol is ambiguous. Alternatively, the use of $E$ is context dependent
The truth is a little mundane: by convention (and please, always follow this if you are writing expectations), in $E[h(A)]$, the expectation is wrt the joint distribution of A; that is the full probability space that the RVs are embedded in.
Mechanistically, this means that your probability density will be a joint probability distribution over all variables in the expectation.
P.S. It’s also my father’s birthday today! Happy birthday! :)