Prove that the sample variance equals $\frac{1}{2 n(n-1)} \sum_{j \neq k}\left(Y_{j}-Y_{k}\right)^{2}$
122149
How to prove that $\sum_{i<j}(X_i-X_j)^2=n\sum_{i=1}^{n}(X_i-\bar{X})^2$
32510
Proving the convergence of $\sum_{n\geq 2}\log\left(1-\frac{1}{n^2}\right)$
18046
Prove the following equality: $\sum_{k=0}^n\binom {n-k }{k} = F_n$
127459
Approximating a multinomial as $p(\xi_1,\ldots,\xi_N)\propto\exp\left(-\frac{n}{2}\sum_{i=1}^N\frac{(\xi_i-p_i)^2}{p_i}\right)$
107335
Prove equality between binomial coefficients.
128913
A proof of $\sum_{i=1}^{n}(-1)^{i-1}\binom{n}{i}\frac{1}{i}=\frac{1}{1}+\frac{1}{2}+....+\frac{1}{n}$
15530
Variance of sample mean.
73189
Proving Bernoulli is the limit of Beta
111951
Prove $\binom{n}{m}\binom{m}{k} = \binom{n}{k}\binom{n-k}{m-k}$
20863
how do I prove this inequallity?
157898
Showing that $\sum_{i=1}^n \frac{1}{i} \geq \log{n}$
106281
Prove $\lim\limits_{n\to \infty}\frac{1}{\sqrt n}\left|\sum\limits_{k=1}^n (-1)^k\sqrt k\right|= \frac{1}{2}$
23246
Challenge question; How do I prove the expected value of the following?
123850
Sample variance derivation
61670
Proving that $(b_n) \to b$ implies $\left(\frac{1}{b_n}\right) \to \frac{1}{b}$
94058
Applying the Berry-Esseen theorem to non-identically distributed summands
83457
Given the pdf $f(y\mid\theta) = \theta y^{\theta - 1}1_{0<y<1}$, show $E\left(\frac{1}{2\theta\sum_{i = 1}^n W_i}\right) = \frac{1}{2(n-1)}$