Question

Show that $E[1/X] = 1/E[X]$ using Jensen's inequality

score 3.5k · Answer 1 · 2018-06-25 21:21:33

3.5k

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Show that $E[1/X] = 1/E[X]$ using Jensen's inequality

Published on 25 Jun 2018 - 21:21

score 131 · Answer 2 · 2018-06-27 09:08:21

131

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Denominator in Jensen's inequality

Published on 27 Jun 2018 - 9:08

score 199 · Answer 3 · 2018-07-06 13:28:35

199

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Proof verification in a general case of an hard inequality

Published on 06 Jul 2018 - 13:28

score 213 · Answer 4 · 2018-07-15 21:28:17

213

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Can we always find a convex combination of a given set of points to satisfy this condition?

Published on 15 Jul 2018 - 21:28

score 457 · Answer 5 · 2018-07-27 20:46:10

457

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Does Jensen's Inequality hold for complex numbers?

Published on 27 Jul 2018 - 20:46

score 59 · Answer 6 · 2018-07-31 18:22:41

59

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Jensen's inequality applied to Liapunov's CLT condition

Published on 31 Jul 2018 - 18:22

score 160 · Answer 7 · 2018-08-01 16:46:03

160

Views

For positive real numbers $x,y,z$, Prove that

Published on 01 Aug 2018 - 16:46

score 108 · Answer 8 · 2018-08-03 19:21:51

108

Views

How to show that $f(x) = a^x$ is convex for $x \in \mathbb R$ using Jensen's inequality?

Published on 03 Aug 2018 - 19:21

score 80 · Answer 9 · 2018-08-07 10:39:37

80

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Generalization of $f\left(\frac{x_1 + x_2}{2}\right) < {f(x_1) + f(x_2) \over 2}$ for odd number of variables.

Published on 07 Aug 2018 - 10:39

score 126 · Answer 10 · 2018-08-27 08:45:27

126

Views

How to introduce weights for Jensen's inequality into $log\sum\sum$

Published on 27 Aug 2018 - 8:45

score 2.4k · Answer 11 · 2018-08-30 02:18:30

2.4k

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Prove that $(1+x)^\frac{1}{x}+(1+\frac{1}{x})^x \leq 4$

Published on 30 Aug 2018 - 2:18

score 341 · Answer 12 · 2018-09-12 15:26:42

341

Views

P.T. $\frac{1}{a^3(b+c)} +\frac{1}{b^3(a+c)}+\frac{1}{c^3(a+b)} \ge \frac 32$

Published on 12 Sep 2018 - 15:26

score 126 · Answer 13 · 2018-09-16 07:53:17

126

Views

Show that $\sum_{\text{cyc}} \frac{1}{b^2+c^2+5bc-a^2} \leq \frac{\sqrt3}{8S}$ for a triangle with sides $a$, $b$, $c$ and area $S$

Published on 16 Sep 2018 - 7:53

score 220 · Answer 14 · 2018-09-26 19:45:31

220

Views

Bounding the variance of the maximum of convex functions of a random variable

Published on 26 Sep 2018 - 19:45

score 156 · Answer 15 · 2018-09-28 13:58:56

156

Views

Prove: for all $x \in (0, 1], 2^x+2^{\frac{1}{x}} \leqslant 2^{x+\frac{1}{x}}$

Published on 28 Sep 2018 - 13:58

List Question

Show that $E[1/X] = 1/E[X]$ using Jensen's inequality

Denominator in Jensen's inequality

Proof verification in a general case of an hard inequality

Can we always find a convex combination of a given set of points to satisfy this condition?

Does Jensen's Inequality hold for complex numbers?

Jensen's inequality applied to Liapunov's CLT condition

For positive real numbers $x,y,z$, Prove that

How to show that $f(x) = a^x$ is convex for $x \in \mathbb R$ using Jensen's inequality?

Generalization of $f\left(\frac{x_1 + x_2}{2}\right) < {f(x_1) + f(x_2) \over 2}$ for odd number of variables.

How to introduce weights for Jensen's inequality into $log\sum\sum$

Prove that $(1+x)^\frac{1}{x}+(1+\frac{1}{x})^x \leq 4$

P.T. $\frac{1}{a^3(b+c)} +\frac{1}{b^3(a+c)}+\frac{1}{c^3(a+b)} \ge \frac 32$

Show that $\sum_{\text{cyc}} \frac{1}{b^2+c^2+5bc-a^2} \leq \frac{\sqrt3}{8S}$ for a triangle with sides $a$, $b$, $c$ and area $S$

Bounding the variance of the maximum of convex functions of a random variable

Prove: for all $x \in (0, 1], 2^x+2^{\frac{1}{x}} \leqslant 2^{x+\frac{1}{x}}$

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