Prove that for any random variable Z taking values in the range {1, 2, 3, . . .}, E(Z) = (Σ from i = 1 to infinity) P(Z ≥ i)?
43861
Find the Mean for Non-Negative Integer-Valued Random Variable
51869
Why does $\;\lim_{n\to \infty }\frac{n}{n!^{1/n}}=e$?
11465
Expected value of $\max\{X_1,\ldots,X_n\}$ where $X_i$ are iid uniform.
82323
Poisson random variables and Binomial Theorem
64844
Finding $E(|X_1|\ |\max |X_i| )$
24683
For i.i.d. $\{X_n\}$ proving $\frac1n\max\limits_{1\leqslant k\leqslant n}|X_k|\xrightarrow{\mathrm{a.s.}}0\Leftrightarrow E(|X_1|)<+∞$
118195
How does one prove that $e$ exists?
27347
Verify that $\left|\int_{\gamma} \exp(iz^2)dz\right| \leq \frac{\pi\big(1-\exp(-r^2)\big)}{4r}$ where $\gamma(t)=re^{it}$, for $0\leq t \leq \pi/4$.
49128
How to prove $\lim\limits_{n \to \infty} (1+\frac1n)^n = e$?
92569
Showing that ${\rm E}[X]=\sum_{k=0}^\infty P(X>k)$ for a discrete random variable
72132
Expected Value of a Hypergeometric Random Variable
133723
Probability of lim sup, lim inf for sequence of random variables.
140790
Prove that $E(X) = \int_{0}^{\infty} P(X>x)\,dx = \int_{0}^{\infty} (1-F_X(x))\,dx$.
13831
Find $ P(Z>X+Y)$ where $X,Y,Z \sim U(0,1)$ independently
85818
$E(|X-Y|)$ for $X$, $Y$ i.i.d and uniform on $[0,1]$
116975
Given $X$ and $Y$ are independent N(0,1) random variables and $Z = \sqrt{X^2+Y^2}$ from the marginal pdf of $Z$
78754
Showing that $E[X|X<x]$ is smaller or equal than $E[X]$ for all x