Jensen's Inequality proof

[baqerjawadal-lawati]

Simplicity is the ultimate sophistication. Thank you for showing that.

[mayankjangid]

Finally got the intuitive reasoning of the inequality ! Thank you so much sir!

[Issara]

All of a sudden utility maximization under uncertainty makes so much more sense now. Thank you good sir.

[solfeinberg]

So clear, such an efficient proof - thank you for informing me and respecting my time and intelligence. Bravo!

[prestonhansen]

Thanks a bunch for the video, this is a lot easier to follow and less notation heavy than the proofs from my course!

[jacobschuster]

Such a clean and intuitive way of proving this. Thanks!

[emrglr]

great way of proving this, thank you!

[고강현-td]

Doesn't L[E(x)]=g(E(x)) only hold if the x is the particular point where g(x) and L(x) meet? Generally, L[E(x)]=<g(E(x)) should hold. Therefore it does not prove the jensen's inequality i think

[dinaashraf]

That's really informative and easy to be understood. Thank you.

[pinkquinn]

Brilliant. It is much easier than I thought :))

[activision]

Would this also imply the reverse is true for a concave function?
I.e., g(E(x)) > E[g(x)] ?

[krstev]

Do you know how complex is the induction proof?

[andrewrochman]

how cool it is i can actually find minimum values of trigonometric functions in a triangle by using jensons inequality

[TheRyry]

This is great. Never seen Jensen's proved in this manner before.

[samuelbarham]

Oh that's such a beautiful proof.

[iamoo]

Thank you! Couldn't understand explanations from the Blitzstein's book..

[barosderiche]

Thanks but not rigorous. A convex function is not necessarily differentiable. Thus there may not exist a tangent line at all.