Question

$\sum_{i=1}^{n}(c_i\log_2 x_i)$ biggest when $x_i = \frac{c_i}{\sum_i c_i}$

score 76 · Answer 1 · 2022-04-17 12:04:47

76

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$\sum_{i=1}^{n}(c_i\log_2 x_i)$ biggest when $x_i = \frac{c_i}{\sum_i c_i}$

Published on 17 Apr 2022 - 12:04

score 969 · Answer 2 · 2022-04-17 21:21:05

969

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Jensen's Inequality Proof for Conditional Expectation (Durrett)

Published on 17 Apr 2022 - 21:21

score 34 · Answer 3 · 2022-04-20 13:40:02

34

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Positive random variables with harmonic mean equal to mean have variance zero

Published on 20 Apr 2022 - 13:40

score 72 · Answer 4 · 2022-04-24 20:38:54

72

Views

prove modified jensen's inequality

Published on 24 Apr 2022 - 20:38

score 103 · Answer 5 · 2022-05-11 09:04:09

103

Views

Simple yet hard inequality with Lipschitz functions

Published on 11 May 2022 - 9:04

score 163 · Answer 6 · 2022-05-16 20:00:17

163

Views

Using Jensen's inequality on $\mathbb{E}[1/x]$ when x can be both positive and negative

Published on 16 May 2022 - 20:00

score 147 · Answer 7 · 2022-05-21 19:09:04

147

Views

If $\sum_{cyc}\frac{a}{a+1}=1$ Show that $abc\le \frac{1}{8}$

Published on 21 May 2022 - 19:09

score 109 · Answer 8 · 2026-03-26 01:12:44

109

Views

About the conjecture $\frac{a^{4}}{133a^{3}+81b^{3}}+\frac{b^{3}}{133b^{3}+81c^{3}}+\frac{c^{4}}{133c^{3}+81a^{3}}-\frac{(a+\sqrt{b}+c)}{214}\ge 0$

Published on 26 Mar 2026 - 1:12

score 106 · Answer 9 · 2022-06-01 09:39:24

106

Views

How to evaluate the following integral might be related to the modified Bessel Function of first kind?

Published on 01 Jun 2022 - 9:39

score 53 · Answer 10 · 2022-06-19 19:46:18

53

Views

An extension on Jensen inequality

Published on 19 Jun 2022 - 19:46

score 524 · Answer 11 · 2022-07-01 11:46:25

524

Views

An Inverse Jensen Inequality

Published on 01 Jul 2022 - 11:46

score 164 · Answer 12 · 2022-07-18 11:01:33

164

Views

$\int f \;d\mu=\int g \;d\mu=1$ and $f \log g \in L^1(\mu)$ implies $\int f \log g \; d\mu\leq \int f \log f \; d\mu$

Published on 18 Jul 2022 - 11:01

score 50 · Answer 13 · 2022-07-20 09:03:24

50

Views

On a property of convex functions

Published on 20 Jul 2022 - 9:03

score 499 · Answer 14 · 2022-07-27 04:40:01

499

Views

What does the abbreviation NB mean?

Published on 27 Jul 2022 - 4:40

score 93 · Answer 15 · 2022-07-30 02:25:40

93

Views

Is $\mathbb{E}(X^{\alpha+1} \ln X) \mathbb{E}(X^\alpha) \ge \mathbb{E}(X^{\alpha+1}) \mathbb{E}(X^\alpha \ln X)$ true?

Published on 30 Jul 2022 - 2:25

List Question

$\sum_{i=1}^{n}(c_i\log_2 x_i)$ biggest when $x_i = \frac{c_i}{\sum_i c_i}$

Jensen's Inequality Proof for Conditional Expectation (Durrett)

Positive random variables with harmonic mean equal to mean have variance zero

prove modified jensen's inequality

Simple yet hard inequality with Lipschitz functions

Using Jensen's inequality on $\mathbb{E}[1/x]$ when x can be both positive and negative

If $\sum_{cyc}\frac{a}{a+1}=1$ Show that $abc\le \frac{1}{8}$

About the conjecture $\frac{a^{4}}{133a^{3}+81b^{3}}+\frac{b^{3}}{133b^{3}+81c^{3}}+\frac{c^{4}}{133c^{3}+81a^{3}}-\frac{(a+\sqrt{b}+c)}{214}\ge 0$

How to evaluate the following integral might be related to the modified Bessel Function of first kind?

An extension on Jensen inequality

An Inverse Jensen Inequality

$\int f \;d\mu=\int g \;d\mu=1$ and $f \log g \in L^1(\mu)$ implies $\int f \log g \; d\mu\leq \int f \log f \; d\mu$

On a property of convex functions

What does the abbreviation NB mean?

Is $\mathbb{E}(X^{\alpha+1} \ln X) \mathbb{E}(X^\alpha) \ge \mathbb{E}(X^{\alpha+1}) \mathbb{E}(X^\alpha \ln X)$ true?

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