Does expectation of a r.v. always converge? Let X be a random variable. Will its expectation E[X] expressed as a (possibly infinite) sum converge for arbitrary X?  My intuition would be yes. Since E[X] is a function of a r.v., E[X] is a r.v. itself, so by definition it maps to the reals. The infinity is not a real number, so there will be a limit to which the E[X] will converge.  Of course you can construe a r.v. such that weighted sum will diverge, but is then the case that E[X] = $\infty$ or is E[X] said to be undefined?
Why does the Cauchy distribution have no mean? From the distribution density function we could identify a mean (=0) for Cauchy distribution just like the graph below shows. But why do we say Cauchy distribution has no mean?
I'm having trouble with a proof by induction I have less than 3000 rep on StackOverflow. Now that the new closing changes are live, I cannot supply a custom off topic message:    I can enter a custom off topic flag message without issue here on meta, though it only has three canned off topic reasons, rather than five.  I'm not sure if this is the same for users with enough rep to vote to close directly, but the lack of a custom message eliminates the ability to use the correct flag reason in some cases.  For example, I wanted to flag , which is simply off topic on SO. However, I can't use a custom message, and none of the canned ones are appropriate.    appears to be the most up to date official information on custom reasons, and indicates that they are remaining in play for now.  supports that.  If this is by design, how should I flag such questions? This is not a case worth bothering the mods over, so I don't want to use a custom diamond attention flag. How run a .jar file with a double-click? I have a problem running .jar files by double-clicking them. When I go to the Properties dialogue I can't find Java--only Archive Manager in the list of programs. But java -jar somefile.jar opens the program. Views indicator inaccurate, shows one views on question with two close votes Two close votes and only one person has viewed the question?    How did this happen? I only get four video output options Using restroom on airplane while fasten seatbelt light is on? This question about  over on  made me wonder what a passenger is supposed to do when they urgently have to use the restroom while the fasten seat belt light is on. FAA regulations require passengers to obey the seat-belt sign, even if flight attendants do not.  I saw this happen on a flight where an older gentleman asked the flight attendant if he could use the restroom, and she said "not until the light is off". The flight had been free of turbulence for 15 minutes or so by this time, and the flight attendants were walking freely throughout the cabin, collecting post-meal trash, etc. The gentleman who asked to use the restroom appeared to be in quite some discomfort, and practically ran to the restroom when the light went off 10 minutes later.  So what is a passenger supposed to do when he isn't permitted to use the lavatory, when he has to go and can't wait? Just go in their seat? How do I give text or an image a transparent background using CSS? Greek Text (babel) and English Code Text (listings): Problem I use the babel package in order to write in greek with font "kerkis".  I want to add code in english ("courier new" font) to my latex document but I get some difficulties.  Can anybody help me, please. Thank you in advance.  \documentclass[12pt]{article} \usepackage[english,greek]{babel} \usepackage[utf8x]{inputenc} \usepackage{graphicx} \usepackage{fancybox} \usepackage{verbatim} \usepackage{courier} \usepackage{kerkis} \usepackage{float} \usepackage{geometry} \usepackage{fancyhdr} \usepackage{titlesec} \usepackage{tocloft} \usepackage{hyperref} \usepackage{afterpage} \usepackage{color}    \usepackage{listings}  \renewcommand{\lstlistingname}{Κώδικας}  \lstset{  %matlab   backgroundcolor=\color{white},     basicstyle=\normalsize,    % COURIER NEW?        commentstyle=\color{green},    % comment style   escapeinside={\%*}{*)},           extendedchars=true,               frame=single,                              keywordstyle=\color{blue},       % keyword style   numbers=left,                     numbersep=5pt,                     numberstyle=\normalsize\color{black},    rulecolor=\color{black},           stepnumber=1,                      stringstyle=\color{magenta},     % string style }   \begin{document}  \selectlanguage{greek} Ελληνικά: \textlatin{this word means greek}  \selectlanguage{english} Now I write in english  \selectlanguage{greek} Ελληνικά  %\selectlanguage{english}???  \begin{lstlisting}[caption = \textlatin{example1.m}] { % Entropy E = 0; for i = 1:J     if p(i) ~= 0         E = E + p(i)*log2(1/p(i));     end end } \end{lstlisting}  \end{document} HTTP vs HTTPS performance Are there any major differences in performance between http and https?  I seem to recall reading that HTTPS can be a fifth as fast as HTTP.  Is this valid with the current generation webservers/browsers?  If so, are there any whitepapers to support it? Restore main APFS container to full disk Would time speed up near a large body of negative mass relative to observers in micro gravity? Time tends to slow down near objects with large amounts of positive mass relative to observers in micro gravity.  Considering that negative mass is the opposite of normal mass and would time tend to speed up near a body of negative mass relative to observers in micro gravity? Can magnets rotate infinitely? Geometric interpretation of Electromagnetism Encopresis: how can we encourage our child to clean himself or ask for help immediately instead of ignoring the dirty underwear? Wasted screen space due to multiple horizontal bars at the top when an application is open in GNOME desktop Prove if $|z| < 1$ and $ |w| < 1$, then $|1-zw^*| \neq 0$ and $| {{z-w} \over {1-zw^*}}| < 1$ Prove if $|z| &lt; 1$ and  $ |w| &lt; 1$, then $|1-zw^*| \neq 0$ and $| {{z-w} \over {1-zw^*}}| &lt; 1$Given that $|1-zw^*|^2 - |z-w|^2 = (1-|z|^2)(1-|w|^2)$I think the first part can be proven by saying $|1-zw^*| = 0$ if and only if $zw^*$ = 1.  And given the conditions that cannot be true. However I don't know if this part is right. How to Map a subset of list elements to a function? Can PostGIS and QGIS provide dependable multi-user editing? After considering a few options, I'm trying to give my 15-20 QGIS 2.2 users the ability to concurrently view/edit one or two basic point PostGIS layers, largest one has just 16,000 records. I've installed PostgreSQL 9.1 / PostGIS 2.0 and basic testing seems to work ok but haven't unleashed it to the masses yet.  We'll typically only have 2-3 editors at a time, but possibly 15 viewers. Edits will all be in QGIS, viewers will be QGIS and ArcGIS (but we don't have SDE).  As I said, these are just basic point files, and  edits will just be adding/deleting points and some table edits. I am not worried about editing the same features at the same time.  Can the combination provide dependable multi-user editing for two basic point files? Breaking a hard-link in-place? I am keeping my dotfiles under version control and the script deploying them creates hard links. I also use etckeeper to put my /etc under version control. Recently I have gotten warnings like this:  warning: hard-linked files could cause problems with bzr   A simple copy (cp filename.ext filename.ext) will not work:  cp: `filename.ext' and `filename.ext' are the same file   Renaming/moving a file - except across volumes - also doesn't break the hard-link.  So my question is: is there a way to break a hard-link to a file without actually having to know where the other hard-link/s to that file is/are? Automatically capitalise the first word in each sentence