Question

Show that $\operatorname{Cov}(X,X^2)=0$ if X is a continuous random variable with symmetric distribution around the origin

score 2.8k · Answer 1 · 2026-03-22 18:47:59

2.8k

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Show that $\operatorname{Cov}(X,X^2)=0$ if X is a continuous random variable with symmetric distribution around the origin

Published on 22 Mar 2026 - 18:47

score 70 · Answer 2 · 2026-03-23 11:30:40

70

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prove that $E(Y) = 0$ if $X$ is a random variable and $Y = x- E(x)$

Published on 23 Mar 2026 - 11:30

score 812 · Answer 3 · 2026-03-23 11:02:47

812

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Limit of the expectation in Galton-Watson-process using a Martingale

Published on 23 Mar 2026 - 11:02

score 519 · Answer 4 · 2026-03-22 15:09:21

519

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Determine if an Estimator is Biased (Unusual Expectation Expression)

Published on 22 Mar 2026 - 15:09

score 240 · Answer 5 · 2026-03-22 19:29:16

240

Views

Why are negative constants removed from variance?

Published on 22 Mar 2026 - 19:29

score 269 · Answer 6 · 2026-03-22 22:15:53

269

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How to find $\mathbb{E}(X\mid\mathbf{1}_{X<Y})$ where $X,Y$ are i.i.d exponential variables?

Published on 22 Mar 2026 - 22:15

score 173 · Answer 7 · 2026-03-23 08:29:13

173

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$X_1,X_2,X_3 \sim^{\text{i.i.d}} R(0,1)$. Find $E(\frac{X_1+X_2}{X_1+X_2+X_3})$

Published on 23 Mar 2026 - 8:29

score 428 · Answer 8 · 2026-03-23 04:30:41

428

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How to calculate the conditional mean of $E(X\mid X<Y)$?

Published on 23 Mar 2026 - 4:30

score 393 · Answer 9 · 2026-03-23 01:24:29

393

Views

Let X be a geometric random variable, show that $E[X(X-1)...(X-r+1)] = \frac{r!(1-p)^r}{p^r}$

Published on 23 Mar 2026 - 1:24

score 155 · Answer 10 · 2026-03-23 04:18:28

155

Views

Taylor expansion of expectation in financial modelling problem

Published on 23 Mar 2026 - 4:18

score 71 · Answer 11 · 2026-03-17 01:42:31

71

Views

Probability question and die rolling

Published on 17 Mar 2026 - 1:42

score 14.2k · Answer 12 · 2026-03-23 00:45:58

14.2k

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Expected value of the absolute value of the difference between two independent uniform random variables?

Published on 23 Mar 2026 - 0:45

score 406 · Answer 13 · 2026-03-23 05:04:33

406

Views

Why does the expected value of $\left[{1\over2}(X_i-X_j)^2-\sigma^2\right] \left[{1\over2}(X_i-X_k)^2-\sigma^2\right]$ equal $(\mu_4-\sigma^4)/4$?

Published on 23 Mar 2026 - 5:04

score 163 · Answer 14 · 2026-03-17 11:38:50

163

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Suggestion for probability problem book

Published on 17 Mar 2026 - 11:38

score 50 · Answer 15 · 2026-03-23 09:29:55

50

Views

When looking at the variance of a function of a r.v. $X$ (say continuous), can you use $Var(g(X)) = E(g(X)^2) - E^2(g(X))$, and then use integration?

Published on 23 Mar 2026 - 9:29

List Question

Show that $\operatorname{Cov}(X,X^2)=0$ if X is a continuous random variable with symmetric distribution around the origin

prove that $E(Y) = 0$ if $X$ is a random variable and $Y = x- E(x)$

Limit of the expectation in Galton-Watson-process using a Martingale

Determine if an Estimator is Biased (Unusual Expectation Expression)

Why are negative constants removed from variance?

How to find $\mathbb{E}(X\mid\mathbf{1}_{X<Y})$ where $X,Y$ are i.i.d exponential variables?

$X_1,X_2,X_3 \sim^{\text{i.i.d}} R(0,1)$. Find $E(\frac{X_1+X_2}{X_1+X_2+X_3})$

How to calculate the conditional mean of $E(X\mid X<Y)$?

Let X be a geometric random variable, show that $E[X(X-1)...(X-r+1)] = \frac{r!(1-p)^r}{p^r}$

Taylor expansion of expectation in financial modelling problem

Probability question and die rolling

Expected value of the absolute value of the difference between two independent uniform random variables?

Why does the expected value of $\left[{1\over2}(X_i-X_j)^2-\sigma^2\right] \left[{1\over2}(X_i-X_k)^2-\sigma^2\right]$ equal $(\mu_4-\sigma^4)/4$?

Suggestion for probability problem book

When looking at the variance of a function of a r.v. $X$ (say continuous), can you use $Var(g(X)) = E(g(X)^2) - E^2(g(X))$, and then use integration?

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