Question

Proof-Check: Reasoning correct to apply Jensen $\mathbb E [X^{p}]\leq \mathbb E [X]^{p}$

score 68 · Answer 1 · 2022-08-21 13:46:20

68

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Proof-Check: Reasoning correct to apply Jensen $\mathbb E [X^{p}]\leq \mathbb E [X]^{p}$

Published on 21 Aug 2022 - 13:46

score 65 · Answer 2 · 2022-09-19 15:53:21

65

Views

Integrability condition in Jensen's inequality

Published on 19 Sep 2022 - 15:53

score 124 · Answer 3 · 2022-09-29 01:23:30

124

Views

Converse to Jensen's inequality for $1/x$ on a positive bounded interval?

Published on 29 Sep 2022 - 1:23

score 393 · Answer 4 · 2022-09-29 13:08:32

393

Views

Any reference on Jensen inequality for measurable convex functions on a Banach space?

Published on 29 Sep 2022 - 13:08

score 68 · Answer 5 · 2022-10-08 00:22:35

68

Views

Jensen's for continuous convex combinations

Published on 08 Oct 2022 - 0:22

score 95 · Answer 6 · 2022-10-16 04:43:06

95

Views

Is $C^2$ necessary for convexity $\implies$ $f''(x) \geq 0$?

Published on 16 Oct 2022 - 4:43

score 60 · Answer 7 · 2022-12-03 08:16:54

60

Views

$ \mathbb P[X > 0] \geq \frac{\mathbb E [X]^ 2}{ \mathbb E [X^2]}$ if the mean is positive and finite

Published on 03 Dec 2022 - 8:16

score 92 · Answer 8 · 2022-12-12 19:04:52

92

Views

Jensen's inequality but with geometric mean

Published on 12 Dec 2022 - 19:04

score 35 · Answer 9 · 2022-12-17 11:32:06

35

Views

Counterexample for Jensen's inequality for rank one convex function

Published on 17 Dec 2022 - 11:32

score 80 · Answer 10 · 2022-12-22 16:02:49

80

Views

Application of Jensen Inequality for lower bound

Published on 22 Dec 2022 - 16:02

score 218 · Answer 11 · 2022-12-28 06:58:25

218

Views

What's the relation between the expectation of p-norm squared of a random vector before and after centering?

Published on 28 Dec 2022 - 6:58

score 136 · Answer 12 · 2026-03-25 11:27:15

136

Views

$f(x)=\sqrt{a\sin^2(x) +b\cos^2(x)+c} +\sqrt{a\cos^2(x)+b\sin^2(x)+c}$, Prove that $\sqrt{a+ c} + \sqrt{b + c} \le f(x) \le 2\sqrt{\frac{a+ b}{2}+c}$

Published on 25 Mar 2026 - 11:27

score 215 · Answer 13 · 2023-01-11 07:36:00

215

Views

Prove that $ \frac{x^2}{1+x} + \frac{y^2}{1+y} + \frac{z^2}{1+z} \geq \frac{1}{2} $

Published on 11 Jan 2023 - 7:36

score 120 · Answer 14 · 2023-01-16 15:09:55

120

Views

A 'continuous version' of Jensen's inequality

Published on 16 Jan 2023 - 15:09

score 32 · Answer 15 · 2023-01-17 20:58:44

32

Views

Upper Bounding A Sum of Powers of Degrees in a Graph

Published on 17 Jan 2023 - 20:58

List Question

Proof-Check: Reasoning correct to apply Jensen $\mathbb E [X^{p}]\leq \mathbb E [X]^{p}$

Integrability condition in Jensen's inequality

Converse to Jensen's inequality for $1/x$ on a positive bounded interval?

Any reference on Jensen inequality for measurable convex functions on a Banach space?

Jensen's for continuous convex combinations

Is $C^2$ necessary for convexity $\implies$ $f''(x) \geq 0$?

$ \mathbb P[X > 0] \geq \frac{\mathbb E [X]^ 2}{ \mathbb E [X^2]}$ if the mean is positive and finite

Jensen's inequality but with geometric mean

Counterexample for Jensen's inequality for rank one convex function

Application of Jensen Inequality for lower bound

What's the relation between the expectation of p-norm squared of a random vector before and after centering?

$f(x)=\sqrt{a\sin^2(x) +b\cos^2(x)+c} +\sqrt{a\cos^2(x)+b\sin^2(x)+c}$, Prove that $\sqrt{a+ c} + \sqrt{b + c} \le f(x) \le 2\sqrt{\frac{a+ b}{2}+c}$

Prove that $ \frac{x^2}{1+x} + \frac{y^2}{1+y} + \frac{z^2}{1+z} \geq \frac{1}{2} $

A 'continuous version' of Jensen's inequality

Upper Bounding A Sum of Powers of Degrees in a Graph

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