Variance is defined as $$V(X) = \sum (x-\mu)^2 .p(x)$$ And standard deviation is $\sigma_X = \sqrt{V(x)}$  But I feel it makes more sense to define $\sigma_X$ as $\sum( |x-\mu|.p(x))$ instead because the mod takes care of negative distances and multiplication by p(x) would give us expected value of the deviation we should expect. Then why is SD defined the way it is?
Let's take the numbers 0-10.  Their mean is 5, and the individual deviations from 5 are -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 And so the average (magnitude of) deviation from the mean is $30/11 \approx 2.72$.  However, this is not the standard deviation.  The standard deviation is $\sqrt{10} \approx 3.16$.  The first mean-deviation is a simpler and by far more intuitive definition of the "standard-deviation", so I'm sure it's the first definition statisticians worked with.  However, for some reason they decided to adopt the second definition instead.  What is the reasoning behind that decision?
In a LaTeX article, the math characters are more "curvy" than the text characters:  \documentclass[12pt]{article} \begin{document}  $x^2 + y^2 = z^2$ \end{document}     In a beamer presentation, the math characters do not have the same curves:  \documentclass{beamer} \begin{document} \begin{frame}  $x^2 + y^2 = z^2$ \end{frame} \end{document}     Question  How can I get the beamer math to look just like the article math?  I would prefer if the solution was a single line (that I could place at the top of my LaTeX file) as opposed to something that needs to appear next to every piece of math. Getting higher power output by using more resistors Expected value as a function of quantiles? Application-priority based automatic bandwidth distribution in Windows? Whenever my browser wants to download data, I want it to be granted as much of the bandwidth as it wants, while other applications must do with the leftover bandwidth; and when the browser is not transferring any data, other applications could be given the bandwidth. Something like the process priority in Windows task manager. Any method/software to accomplish this automatically? System calls supported in running Kernel Is there a way to get the number of or list of system calls supported by currently running Linux Kernel? So I want to find a way to 'read' the syscall table of a running kernel. Transferring domain to new host, but keeping email on old host I'm helping out a friend manage his website. Said friend has a domain, website.com, which I am transferring from his old host (OLD) to his new host (NEW), but OLD does not provide email services (or, at least, not intuitively). As a result, he wants both:   To host the website at NEW To use the email servers at OLD so he can continue using the email accounts he set up there.   The move from OLD to NEW has taken place, and I have updated the DNS records so they no longer point at ns1.old.com, and now point instead at ns1.new.com, and so on.  But having searched around a bit for the solution to the email aspect, I'm a little uncertain. I've updated the MX record at NEW to point back to ns1.OLD.com, but emails are still failing - and I'm sure the reason for this is obvious, but I'm not quite grasping what I need to do here.  As I understand it, the process ought to be as follows:   Mail sent to account@website.com website.com routes the mail to the host at NEW NEW then uses the new MX record to rout it to the servers at OLD Hey presto, the email should appear in the email inbox at account@website.com at OLD.   But this isn't happening. I get a 550 error telling me to turn on SMTP authentication, which I've read is a sure sign that I've got the MX configuration wrong. Any assistance on this would be really greatly appreciated.  tl;dr: Friend wants to move site hosting to NEW, but keep email hosting at OLD - I don't know what to do with MX and nameservers and so on to make this happen. how to crop image in to pieces programmatically How can I find my Bug-report that I submitted from the Desktop on launchpad?  I have found a partial solution to my own question:  The program that sends the Bug-reports from the desktop is called apport. It doesn't requires a launchpad account. The service whoopsie submits the Bug-Report directly to the server daisy.ubuntu.com (I'm not sure if those bugs actually appear on launchpad publicly.)  But I found my Bug-Report on my Harddisk in /var/crash/ .  From there I can copy and paste parts of the file to my opened bug on launchpad. Thanks for your tips.  Original question:  I had a severe bug, and I found someone with the same problem in launchpad. After I found a temporary fix I was able to submit the bug with the ubuntu-bug-reporter.  How can I find this ubuntu-bug-reporter generated bug-report in launchpad? I would like to combine those two bug-reports (mark as duplicate). Because the generated one has all the debug information and the other one has the description of this bug. OL3 How to select features of a WMS layer I have been using the app for 3 days now. I just opened it up again, and it asked me to sign "up" again with either Google or the Trainer server.   So I signed up with the same Google account as when I first started with and the game started again.   Is there Any way I can get my progress back? What is a magic number, and why is it bad? What is a magic number?  Why should it be avoided?  Are there cases where it's appropriate? The Quotation Mark character in TeXworks editor has vanished Now, my version of TeXworks is 0.4.5r.1280 and I can't have the " character on the keyboard.    I have ``  or '' instead. Why?  And It's the same with Alt+034. I'm very disappointed with that. Were there any canon examples of Harry being an innately powerful wizard? Was Harry Potter an innately powerful/skillful Wizard in any way, based on canon?  It seems that whenever Harry Potter performed some unusually potent bit of magic (potent as far as require raw power AND/OR skill), most of the time we find that it wasn’t innately Harry’s skill, but a combination of:   some extraneous magic forces/rules/powers circumstance great reaction time (which is obviously extraordinary from his Quidditch playing; and is likely a larger factor in his dueling than the strength of his magic) general smartness or (the part that Harry’s detractors, including Voldemort missed) Harry’s strength of character/personality   The only two counter-examples I can think of which show him as having extraordinary or at least obviously above average magical abilities are:   His skill at flying brooms - while a part of it is pure physical skill, at least part is magical. His (corporeal) Patronus charm   As far as examples of his unusual feats being due to reasons listed above:   Obviously, surviving Avada Kedavra as an infant - due to Lily’s sacrifice Parselmouth talent - proxied via Voldemort’s piece of soul. Ability to see the Sorcerer’s Stone in the Mirror of Erised - due to purity of his character, nothing magical. Obvious lack of talent at potion making throughout all of the books (sans cheating in HBP) His win over the Basilisk - due to Hermione’s research, character traits, and as a consequence of the last one, getting Fawkes and Gryffindor’s Sword’s help.  Just to be clear, before someone flames me - what he did was obviously super extraordinary, BUT IMHO he would have achieved the same result if he was turned into a Squib for the duration of Chamber of Secrets fight. TriWizard Tournament entry - wasn’t him, it was Barty Crouch TriWizard Tournament second challenge - a combination of character and outside help (someone told him about Gillyweed) TriWizard Tournament third challenge - Mostly, Barty Crouch’s cheating  Note that I’m omitting the first challenge, since that one was the aforementioned Broom flying skills. His survival in the cemetery after Voldemort’s return - again, a combination of superior strength of character and super powerful wandlore magic that had nothing to do with his skill as a Wizard. The whole “last Horcrux” thing when surviving the second Avada Kedavra from Voldemort His ownership of the Elder Wand in the very last duel with Voldemort.   So, to paraphrase my original question, was there any canon/JKR evidence that Harry was anything but a completely average/mediocre wizard in any way, shape, or form if you take into account only his own magical abilities and skills? What does size of a directory mean in output of 'ls -l' command? What does size of a directory mean in output of ls -l command? I am a Bangladeshi citizen. Back in 2013, I went to India with a tourist visa and overstayed for four days. It was due to a gout attack in my feet but I don't have my medical papers to prove that.  I applied again in 2015 for a visa, at Dhaka, and they refused my visa and blacklisted my passport, writing some numbers and date on it. Now I am not able to get an Indian visa.  How I can remove my passport from the blacklist and get a new Indian visa? Do I need a Indian immigration lawyer to do this? Resizing videos with ffmpeg/avconv to fit into static sized player I have a html 5 video player which is 700px wide, 400px high. I'm trying to use avconv to use ffmpeg to resize (while retaining the aspect ratio) and making sure it fits into my player.  Input can be a file of any size, so I need to resize the larger ones but center the smaller ones with black bars. So far I've tried: -s and -aspect, I've seen pad being used with the -vf switch but don't understand how it works enough to get what I need.    This is a rough idea of what I need. I'm not sure if it's even possible. It's almost like CSS's max-width/max-height. I realise this may just be a jumble of words but if anyone happens to understand what I'm talking about, I'd appreciate help, Thanks.  avconv command:  avconv -y -i control.avi -vcodec libx264 -b 2000k -bufsize 20M -acodec aac -strict experimental -ar 44100 -ab 256k bigbuck_out.mp4 I have to show that the ring $\mathbb{Z}[X]/(X^2-1)$ is not isomorphic with $\mathbb{Z}\times \mathbb{Z}$.    I know that $(\mathbb{Z}\times\mathbb{Z})^*=\{(\pm1,\pm1)\}$, so I thought I should be looking for elements which have inverses in $\mathbb{Z}[X]/(X^2-1)$ and hopefully find more or less than 4. But I didnt succeed, so I need hints. Thanks. App Store is the wrong language Quickly read the last line of a text file? Were any of the Elves in Tolkien twins? Thinking about the idea of Elves having low numbers overall, got me to wondering: as far as Tolkien's writing, could elves ever have twins?  As a "yes" answer, I need an example of twins (any of JRRT work). They must be full on Elves, not half-Men. As a "no" answer, has to be an explicit statement in his work stating Elves ALWAYS had one child at a time. Anything else is a "maybe, we don't know".