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I recently posted this question and it was quickly closed as off-topic. Could anyone offer any advice as to how this question may be improved, if it is at all salvageable? This will help me with future contributions.

This particular question was not a homework problem (though I miss the days of having homework), but I can certainly see why it may be construed as such, given its simplistic nature.

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    $\begingroup$ I think it's a fine question, but had I encountered it I would have closed it as a duplicate of many other posts. That's not meant in a deprecating way: if you aren't familiar with the Cauchy-Schwarz inequality, you don't know how to search for it. $\endgroup$
    – whuber Mod
    Commented Jun 9, 2023 at 11:51

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At the outset, let me state I wasn't one of the reviewers to vtc your post (I have desisted myself from review work, to digress a bit). So, this would be my quick assessment of the present status of the post.

Your question basically entails (dis)proving an inequality providing a bound to $\mathbb E[XY]$ where both $X, Y$ have the same marginal distribution.

This is a classic problem to be classified as a (which you didn't use) problem. The tag explicitly mentions

A routine exercise designed to test one's knowledge; often from a textbook, course, or test used for a class or self-study. This community's policy is to "provide helpful hints" for such questions rather than complete answers.

They don't necessarily need to be an exact homework or course work problem assigned by your prof, which often though maybe the case; the flavor and tone of the question matters.

The closure reason offers you helpful link to meta posts that offer general advices as to how to frame a workable self-study post.

The crux is that for a homework like problem to be worthy of the site, it needs to show a conceptual query and a genuine effort/approach to solve the problem - show what you have tried.

You apparently proved the relation to be true for some special cases. But then you left the general case, assuming that you couldn't strike any idea how to solve for the general case. But you didn't say why that is so. What are the present tools that you have used to do the same? Or did you?

It needed to elicit more information as to how tried to solve for the general case which was missing - remember we are not asking you to show the solution (that's why the question was asked at the first place) but at least a minimal effort was warranted.

I noted Xi'an did provide a helpful hint in the comment, which you seemed to have used for your problem.

Personally, I would have considered the question as a borderline and might have left it open. But I can up to some extent concur with the reviewers.

As for how you could improve it, let me allure your attention to this meta SO post which shares the general sentiment that one needs to adhere, among them particularly these:

$\bullet$ Search for already existing questions about your issue.

$\bullet$ Help us understand your baseline.

There are other useful threads which you can find helpful but the general spirit is unilaterally same.

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