[throwawaySG]

Do you think that real analysis and measure theory helped you get a better grip on the notion of a r.v. than just the simple function from sample space to real line definition? I'm slightly tempted to take or at least try to self-study real analysis and eventually measure theory, but everyone I know (including profs) has told me not to bother if I'm not going to do theoretical stuff.

[nicolapede]

It depends what you mean by "getting a better grip". There are books on scientific topics that do not rely on technical details. When they are great, they are so exactly because, even with this constraint, they manage to clearly convey the elemental notions to a layman ([0] is a great example). It is debatable whether the grip you get in this way is better or not. Certainly it can get deeper, when complemented with the right analytical tools.

[0] - https://www.amazon.co.uk/Relativity-Routledge-Classics-Bertr...