Is it possible to minimize least absolute deviations (LAD) analytically?  Say given a sample $\{x_i\}_{i=1..n}$ find  $$\arg\min_\lambda{\sum_{i=1}^{n}{|x_i-\lambda|}}$$
Suppose we have a set $S$ of real numbers. Show that   $$\sum_{s\in S}|s-x| $$   is minimal if $x$ is equal to the median.    This is a sample exam question of one of the exams that I need to take and I don't know how to proceed.
Command Shift Period (show hidden files) stop working On my MacBook with OS Mojave, Command Shift Period (show hidden files) stop working. How to restore it?? Thanks in advance! Convert a column into a comma separated list Related questions in "Ask Question" page is better than the search tool My Area51 account crossed 200 rep today, but still other accounts don't reflect the change in reputation. When will the changes be applied? or is there no association bonus for Area51 account? apt-get update fails to fetch files, “Temporary failure resolving …” error Is it possible to see a list of the settlers in a given settlement and the jobs they are assigned to? It would make it easier to pick a settler for a new job. Should a student be penalized for using a theorem outside of the curriculum? What point (pt) font size are \Large etc.? In the preamble I have:  \documentclass[a4paper,11pt]{article} \usepackage{fontspec} \setmainfont{Arial}   What can be inferred about the real font pt size for the following?  \tiny, \scriptsize, \footnotesize, \small, \normalsize, \large, \Large, \LARGE, \huge, \Huge Opposite of Alternatives If $ a$, $ b$, $ x$, $ y$ are integers greater than $1$ such that $ a$ and $ b$ have no common factor except $1$ and $ x^a = y^b$ show that $ x = n^b$, $ y = n^a$ for some integer $ n$ greater than $1$.  I started this way: $x^a=y^b$ $=&gt;$ $x=y^{b/a}=(y^{1/a})^b$. Thus $x$ is an integer, and so is $y^{1/a}$, so $y=n^a$ for some integer $n$ greater than $1$. Then from the given relation, we get $x=n^b$.   I am not very convinced with my solution, as I feel I did some mistake. Can anyone point out where the mistake is? Any other solution is also welcome :) Why are integer literals with leading zeroes interpreted strangely? Need help in the longtable with the figure Graphing y=x^2 and y=x I want to draw the region bounded by y=x^2 and y=x. Any ideas? I was hoping this would be somewhat simple. I've tried used a similar, with \begin{axis}..\end{axis}, but it doesn't like that. Did I not declare a package or something?   Also, if I wanted to show the solid this region creates by rotating it about the x-axis, is there a way to did this in latex? (If you had cal 2, think volume of a solid rotated about ...). Calculating residue of pole of order $2$ Is there a good way to compute the residue of $f(z)=\dfrac{1+z}{1-\sin z}$ at $z=\pi/2$, which is a pole of order $2$?  Using the residue calculation formula yields  $$\text{Res}_{z=\pi/2}f(z)=\lim_{z\rightarrow\pi/2}\dfrac{d}{dz}\left(\left(z-\dfrac\pi2\right)^2f(z)\right)$$  The derivative is quite ugly, and calculating the limit requires L'Hospital probably twice (or more). The calculation is just too much. Is there a better way? expected true to respond to true? How to get GNOME Shell "Applications overview" to show the full name of applications Is a constant condition more costly than switching shaders? The origin of my question arose from a problem: Let $q: X \to Y$ and $r: Y \to Z$ be covering maps, let $p= r \circ q$. Show that if $r^{-1}(z)$ is finite for each $z \in Z$, then $p$ is a covering map.  I am just wondering is there an easy counter example to show the necessary of "inverse image of every point is finite" condition?  I have already checked Hatcher's book (the wedged circle example) but I wonder is there a less complex and more obvious example?  I tried to construct a counter example by composition of a covering map from $R_+$ to $S^1$ with $R$ in the middle, but I failed due to I can't find a covering map from $R^+$ to $R$ which does the job. How should we treat questions that are, or have seeds of, evil or malicious purposes and actions, such as writing spambots and malware?    Should they be answered like regular "everybody keeps their pants on" questions? Or should there be some other type of response to this bad behaviour lot? Disable Ctrl+Alt+Del on Windows 7