Lol

This is my intuition for why Jensen's inequality is true: For E[X^2], the bigger values of x are more important because they get much bigger when you square them, and similarly, the smaller values of x are less important. For E[X]^2, every value of x gets equal importance. Since E[X^2] gives less importance to small values and more importance to large values, it ends up being larger overall.

​@MTGandP I also think the intuition for why it's true isn't nearly as important as why we care that it's true. Like I've watched two videos about it now, and I'm fairly confident that I understand the mechanics of it. I could work out my own problem, but hand or in Python. But so what? I can work this out very well and good, but this doesn't explain why anybody should care that it's true.

That's what I needed

Lol yup

Darkmatter 476 same argument but the inequality is reversed