query: Prove that $\min_{\mu}\sum_{i=1}^n|y_i-\mu|=\text{median}\{y_1,\cdots,y_n\}$
positive_passages.docid: 7740
positive_passages.text: The median minimizes the sum of absolute deviations (the $ {\ell}_{1} $ norm)
negative_passages.docid: 122929
negative_passages.text: Prove that $Y=-2\sum_{i=1}^n \ln F_{X_i}(X_i)$ have distribution $\chi^2(2n)$
negative_passages.docid: 144382
negative_passages.text: Proving $\lVert x \rVert_3$ is smaller than euclidean norm
negative_passages.docid: 93427
negative_passages.text: Show that $\sum_{i=1}^{n} \frac {a_i}{1+a-a_i} + \prod_{i=1}^{n} {(1-a_i)} \leq 1$
negative_passages.docid: 14197
negative_passages.text: show that $\sum_{i=0}^l \dfrac{{l\choose i}}{{n\choose k + i}} = \dfrac{n+1}{(n-l+1) {n-l\choose k}}$
negative_passages.docid: 72813
negative_passages.text: If $X$ and $Y$ are uniformly distributed on $(0,1)$, what is the distribution of $\max(X,Y)/\min(X,Y)$?
negative_passages.docid: 78733
negative_passages.text: Finding the density for $\min\{X, Y\}$
negative_passages.docid: 108298
negative_passages.text: Prove $\sum_{i=1}^{i=n}\frac{a_i}{S-a_i}\geqslant \frac{n}{n-1}$ and $\sum_{i=1}^{i=n}\frac{S-a_i}{a_i}\geqslant n(n-1)$.
negative_passages.docid: 146333
negative_passages.text: Gaussian proof for the sum of squares?
negative_passages.docid: 98941
negative_passages.text: Closed formula for the sums $\sum\limits_{1 \le i_1 < i_2 < \dots < i_k \le n} i_1 i_2 \cdots i_k $?
negative_passages.docid: 34797
negative_passages.text: $E|X-m|$ is minimised at $m$=median
negative_passages.docid: 120422
negative_passages.text: The joint density of the max and min of two independent exponentials
negative_passages.docid: 10483
negative_passages.text: Prove Sylvester rank inequality: $\text{rank}(AB)\ge\text{rank}(A)+\text{rank}(B)-n$
negative_passages.docid: 117907
negative_passages.text: A question regarding independence of $\min{\{X,Y\}}$ and $X-Y$ when $X,Y$ follows iid geometric distribution
negative_passages.docid: 43181
negative_passages.text: What is the joint distribution of $Z=\min(X,Y)$ and $I_{Z=X}$?
negative_passages.docid: 42266
negative_passages.text: Show that $d(x,y)=\min \{1,|x-y|\}$ is a metric on $\mathbb R$
negative_passages.docid: 105268
negative_passages.text: prove inequality through mean value theorem