I suspect the best path forward in this instance is to ask a separate question, not two or more questions, that is a straight-up reference request for work that discusses blah blah blah. If you want to let the conditions on the distributiion (beyond symmetry) be open-ended, that's fine, but if that's the case, then be very upfront about it. The separate question can refer back to the old question.

@ToddTrimble If you agree that $\inf c$ depends on the distribution, so the answer that Iosif provided $\inf c = 2M$ is wrong, because it doesn't depend on the distribution and I can find a distribution for which $\inf c<2M$. Do you get my point here? Now, when we say a quantity depends on the distribution at hand, it means that it depends on some propertis/characteristics of this distribution, like 1st moment, second moment, convexity, continuity, differentiablity, smoothness, "many things".

@ToddTrimble Thanks for your clarification on not taking sides with Iosif, but honestly, even if you did, that's not my concern here. My point here is that I have asked a question and the answer is wrong. I have started with "Let $X$ be an r.v....." then, based on this r.v., I have introduced $\inf c$. So, why is it answered $\inf c = 2M$??? I can find an $X$ for which $\inf c<2M$. Iosif has clearly understood from his 1st comment that $\inf c$ indeed depends on $X$.

@ToddTrimble Btw, apologies for the all caps letters, I initially wanted to type them in bold, but didn't know how, so wrote them in caps. The intention was not yelling at all. Are you saying the question is "open-ended" because it hasn't specified what exact property of the distribution I am looking for? Is it the reason or you are referring to something else?

"Do you get my point here?" Yes, I think I've gotten your point all along. But, so you say his answer is wrong -- well, move along then! Ignore his answer. The reason I entered the discussion is to see whether we can make this a workable question for MO. I already gave some advice in my previous comment. (to be continued)

Yes, as I said, MO questions are most successful when they are precise, with all hypotheses laid out. I'm repeating myself at this point, but "The trouble I think is that with an open-ended question, that hinges on unspecified properties etc., readers will not be sure what it is that you want." I think it would be best if you open a new question and then follow my advice to make this a literature or reference request, and ask it as a single question, but you are free to do as you please.

To make a bold font in comments, put your text between a pair of double-asterisks. To italicize, put it between a pair of single asterisks.

"Ignore his answer." Well, he constantly replies "Your question has been fully answered", one can count the number of times he has typed this...I am maximally focusing now to see exactly what you are advising me here. "readers will not be sure what is it that you want", well I have clearly stated upper/lower bounds on $\inf c$, why shouldn't a reader be sure? I need some $c_1$ and $c_2$ such that $c_1\leq\inf c\leq c_2$. Isn't it obvious?

Thanks for the instruction on fonts. I appreciate.

Now I don't know what properties of distribution these $c_1$ and $c_2$ depend on.

(I assume that you are not asking me to "define" what upper/lower bound is for the audience of this community.)

I don't know how else to say it. "Are you saying the question is "open-ended" because it hasn't specified what exact property of the distribution I am looking for?" Yes, that's more or less what the problem is, I think, and Iosif was trying to say this as well. We should probably stop with the comments under his answer, but we can open up a new chat room to continue. No, you don't have to define basic terms like upper/lower bound; it sounds like you're not getting my point.

Could you please open up a new chat or tell me how to do so? I don't know how these upper bounds depend on the distribution, when I do not know, what can I tell then?

See if you can access this: chat.stackexchange.com/rooms/151910/chat-for-ben-and-todd

Yes, it says be patient while its being processed

I upvoted your question, in order for you to have the 20 points I think you need to enter a chat room. You have a rep of 21 now.

Thank you. Should I do anything specific? refreshing the website? clicking on something?...

What happens when you click the URL I gave you?

Okay, let me see about that.

Try this instead: chat.stackexchange.com/rooms/151912/room-for-ben-and-todd

I entered, but there is no place to type as far as I can see, and at the bottom it sayd I need to have some points to be able to talk

I see your message, but cannot type

Yes, that's why I voted you up. Strange it's not working, but maybe there's a time lag before the rep change fully enters the system. Let's pick this up again later. I have other things I need to attend to now.

Ok, thanks. Do you have a specific time in mind to pick this up again?