Question

Expectation of $Y=X^{6}$ : $X \sim \mathcal{N}(0,1)$?

score 127 · Answer 1 · 2026-03-25 22:26:05

127

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Expectation of $Y=X^{6}$ : $X \sim \mathcal{N}(0,1)$?

Published on 25 Mar 2026 - 22:26

score 86 · Answer 2 · 2020-06-20 10:29:50

86

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Does $\operatorname E[e^{-X}Y]\le c$ imply $\operatorname E[Y]\le c\operatorname E[e^X]$?

Published on 20 Jun 2020 - 10:29

score 215 · Answer 3 · 2020-06-20 11:10:42

215

Views

Application of distance between probability measures

Published on 20 Jun 2020 - 11:10

score 16 · Answer 4 · 2026-03-10 13:08:54

16

Views

Expecation of $S(t)=\sum_{i=1}^{N(t)}(X_i+T_i)^2$ for Poisson process $N(t)$

Published on 10 Mar 2026 - 13:08

score 45 · Answer 5 · 2020-06-20 11:49:06

45

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$\operatorname P\left[X\ge\lambda\right]\le e^{-a\lambda}$ for all $\lambda$ implies $\operatorname E\left[e^X\right]\le\frac a{a-1}$

Published on 20 Jun 2020 - 11:49

score 107 · Answer 6 · 2020-06-20 23:11:17

107

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Shifting index while calculating expected value

Published on 20 Jun 2020 - 23:11

score 85 · Answer 7 · 2020-06-21 01:52:53

85

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Derivation of formula for expected number of flips until k consecutive heads for any p

Published on 21 Jun 2020 - 1:52

score 46 · Answer 8 · 2026-03-29 20:03:22

46

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Expected Euclidean Distance

Published on 29 Mar 2026 - 20:03

score 275 · Answer 9 · 2020-06-21 05:55:31

275

Views

Expected value is defined in terms of probability measure or cumulative distribution function?

Published on 21 Jun 2020 - 5:55

score 75 · Answer 10 · 2020-06-21 15:59:09

75

Views

$X_n \xrightarrow{\mathbb{P}} X \iff \lim_{n \to \infty} \mathbb{E}[\min\{|X_n - X|, 1\}] = 0$

Published on 21 Jun 2020 - 15:59

score 36 · Answer 11 · 2026-03-31 07:09:45

36

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To prove $\operatorname{Cov}(X,Y)=0$ with $X \sim {U}[-1,1]$ and $S$ is sampled from $\{{-1,1}\}$ with $p=0.5$ and $Y=XS$

Published on 31 Mar 2026 - 7:09

score 106 · Answer 12 · 2026-04-03 04:23:09

106

Views

Conditional expectation for coin toss

Published on 03 Apr 2026 - 4:23

score 21 · Answer 13 · 2026-03-29 19:44:46

21

Views

Expected value for random variables based on Poisson distribution

Published on 29 Mar 2026 - 19:44

score 853 · Answer 14 · 2026-04-01 09:33:12

853

Views

Expected value of product of dependent variables.

Published on 01 Apr 2026 - 9:33

score 124 · Answer 15 · 2026-03-30 14:37:44

124

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Bound on the sum with binomial coefficients

Published on 30 Mar 2026 - 14:37

List Question

Expectation of $Y=X^{6}$ : $X \sim \mathcal{N}(0,1)$?

Does $\operatorname E[e^{-X}Y]\le c$ imply $\operatorname E[Y]\le c\operatorname E[e^X]$?

Application of distance between probability measures

Expecation of $S(t)=\sum_{i=1}^{N(t)}(X_i+T_i)^2$ for Poisson process $N(t)$

$\operatorname P\left[X\ge\lambda\right]\le e^{-a\lambda}$ for all $\lambda$ implies $\operatorname E\left[e^X\right]\le\frac a{a-1}$

Shifting index while calculating expected value

Derivation of formula for expected number of flips until k consecutive heads for any p

Expected Euclidean Distance

Expected value is defined in terms of probability measure or cumulative distribution function?

$X_n \xrightarrow{\mathbb{P}} X \iff \lim_{n \to \infty} \mathbb{E}[\min\{|X_n - X|, 1\}] = 0$

To prove $\operatorname{Cov}(X,Y)=0$ with $X \sim {U}[-1,1]$ and $S$ is sampled from $\{{-1,1}\}$ with $p=0.5$ and $Y=XS$

Conditional expectation for coin toss

Expected value for random variables based on Poisson distribution

Expected value of product of dependent variables.

Bound on the sum with binomial coefficients

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