I'm not sure why, but
$$Cov(X,Y) = E\left((X-\mu_X)(Y-\mu_Y)\right)$$
doesn't seem to give me big brackets.
I'm not sure why, but
$$Cov(X,Y) = E\left((X-\mu_X)(Y-\mu_Y)\right)$$
doesn't seem to give me big brackets.
As @user240002 pointed out in a comment, "big" delimiters aren't necessarily big: they merely scale to match their content. If the content doesn't have a lot of height (or depth), they won't scale.
You can override the default sizes using \big, \Big, \bigg and \Bigg; for left and right delimiters it's best to use \bigl and \bigr (entirely analogous variants exist for the rest of the bunch, and if you happen to need something in the middle there's also \bigm).
The downside is that the size won't automatically adjust anymore, of course. So instead, you can also force brackets to be larger: add a \strut to force a certain minimum height/depth, or use a \vphantom{...}. I recommend experimenting here, not just to solve the immediate problem but also to learn a new trick or two that'll surely come in handy in the future.
A few other tips:
$$ ... $$, you use \[ ... \] in LaTeX; see Why is \[ ... \] preferable to $$ ... $$? (that, or use a named environment like equation).statmath is a useful package that has shortcut commands for a number of things you'll need for statistics, including \cov and \E.\Cov), it's recommended to use \DeclareMathOperator from amsmath; see Define additional math operators to be typeset in roman .\mathit, i.e. \mathit{Cov} instead of Cov; that'll give you better spacing.That's all I have.
\[Cov(X,Y) = E\bigl((X-\mu_X)(Y-\mu_Y)\bigr)\]to get bigger brackets. Or\[\operatorname{Cov}(X,Y) = E\bigl((X-\mu_X)(Y-\mu_Y)\bigr)\]– Apr 19 '21 at 03:13