What can we say about $\mathbb{E} \left(\frac{1}{\sum_{i=1}^N X_i}\right)$?
42861
Inverse of sum of exponential random variables (mean and variance)
62605
How to find $\mathbb{E}(X\mid\mathbf{1}_{X<Y})$ where $X,Y$ are i.i.d exponential variables?
73865
Find $\lim_{n\to\infty}n\left(\sum_{i=1}^{n}\dfrac{1}{(n+i)^2}\right)$
71743
$\lim (1+\frac{1}{n+1})^n = e$
135731
Is there a way to show that $e^x=\lim_{n\to \infty }\left(1+\frac{x}{n}\right)^n$?
154506
Evaluating $\lim_{n\rightarrow\infty} (\frac{(1+\frac{1}{n})^n}{e})^n$
8606
Calculate $\int^{n+1}_1 \frac{(\{x\})^{[x]}}{[x]}dx$ where $n\in\mathbb{N}$, $[x]$ is the integer part of $x$ and $\left\{ x\right\} =x-[x]$.
43538
Show $\lim_{n \to \infty} n^{-1} E \left( \frac{1}{X}1_{[X>n^{-1}]} \right) =0$
61659
How to show that $ \sum_{n = 0}^{\infty} \frac {1}{n!} = e$?
157898
Showing that $\sum_{i=1}^n \frac{1}{i} \geq \log{n}$
23217
About $\lim \left(1+\frac {x}{n}\right)^n$
104365
Evaluate: $\lim_{n\to\infty}\left({2\sqrt n}-\sum_{k=1}^n\frac1{\sqrt k}\right)$
74054
Conditional expectation for a sum of iid random variables: $E(\xi\mid\xi+\eta)=E(\eta\mid\xi+\eta)=\frac{\xi+\eta}{2}$
5034
A closed form of $\int_0^1\frac{\ln\ln\left({1}/{x}\right)}{x^2-x+1}\mathrm dx$
153056
From where term $\left(\frac{1}{n}+\frac{1}{m}\right)$ came in estimated variance of $\bar x - \bar y$
152184
Find expectation of $\frac{X_1 + \cdots + X_m}{X_1 + \cdots + X_n}$ when $X_1,\ldots,X_n$ are i.i.d
26226
Proving $\lim \limits_{n\to +\infty } \left(1+\frac{x}{n}\right)^n=\text{e}^x$.