Prove that $E[X|X]=X$
134696
How can I show that the conditional expectation $E(X\mid X)=X$?
42143
Prove X is a martingale
23246
Challenge question; How do I prove the expected value of the following?
138962
$X$ is a random variable, if $\Bbb E(X^2)=1$ and $\Bbb E(X)\geq a>0$, prove that $\Bbb P(X\geq\lambda a)\geq(a-\lambda a)^2$ for $0\leq\lambda\leq 1$.
140988
Prove $\exp(x)\exp(y)=\exp(y)\exp(x)$ if $[x,y]=0$.
140790
Prove that $E(X) = \int_{0}^{\infty} P(X>x)\,dx = \int_{0}^{\infty} (1-F_X(x))\,dx$.
46056
If $\mathcal{E}$ are subsets of $X$ and $A \subset X$. Show that $\mathcal{A}\mathcal{(E \cap}$ A)=$\mathcal{A}\mathcal{(E)} \cap$ A
42193
Show that $E(Y^p)=\int_{0}^{\infty}px^{p-1}P(Y\geq x)dx$
64844
Finding $E(|X_1|\ |\max |X_i| )$
101792
By expanding $e^x$ into a series prove the following inequality
130854
Constructing example showing $\mathbb{E}(X^{-1})=(\mathbb{E}(X))^{-1}$
662
If $E[X|Y]=Y$ almost surely and $E[Y|X]=X$ almost surely then $X=Y$ almost surely
16253
Proof that $|\sin(nx)| \le n|\sin(x)|$
123555
Proving that if $ab=e$ then $ba=e$
67489
How to show that $E[(\hat\theta -\theta)^2]<Var(\bar X)=\dfrac{1}{n}$?
107058
Prove that $E(X\ln X)\le E X E\ln X$
132920
Help with proof that the expected value of $x_i$ is $\bar{X}$