Symmetry of distribution function is defined as $f(x-a)=f(-(x-a))$, then expectation is $'a'$. i.e $E(X)=a$
48693
Central Moments of Symmetric Distributions
42193
Show that $E(Y^p)=\int_{0}^{\infty}px^{p-1}P(Y\geq x)dx$
1301
Expected value and standard deviation of $X^2$ in terms of moments of $X$
4064
An equality involving the mean value property
102030
Getting the expectation symbol to behave like $\sum$ instead of $\Sigma$
141861
What is meant by the variance of *functions* in *Introduction to Statistical Learning*?
42024
What is the distribution function of $\left( \begin{smallmatrix} X \\ (-1)^nX \\ \end{smallmatrix}\right)$ where $X\sim N(0,1)$
78754
Showing that $E[X|X<x]$ is smaller or equal than $E[X]$ for all x
121494
Invariance, covariance and symmetry
115242
For a distribution function $F(x)$ and constant $a$, integral of $F(x + a) - F(x)$ is $a$.
27788
Why is the expected value $E(X^2) \neq E(X)^2$?
151157
Justification of proof of law of total expectation
32578
Skew-symmetric function
64493
$X$ is a Geometric random variable find the expectation of $1/X$
38324
Show that $E(X)=\int_{0}^{\infty}P(X\ge x)\,dx$ for non-negative random variable $X$
5350
Explain why $E(|X|^p)=p\int_{0}^{\infty}y^{p-1}P(|X|>y) dy$
114603
Conditional Expectation of Composite Function