Meaning of Likelihood in layman's terms
What is the difference between "likelihood" and "probability"?
Proof using Prüfer encoding The question is as below:      Show that each vertex $v$ of a tree $T$ appears $deg(v)-1$ times in the Prüfer encoding of $T$, where $deg(v)$ is the degree of $v$ in $T$.   For this, I think there are 3 scenarios a leaf should be considered for: (1) when it is a leaf as part of a tree; (2) a leaf that has been discarded; (3) the remaining edge. I feel like this will result in a short proof which is only two (or so) statements long, but at the same time, feel it is too simple.   EDIT: I've had a look at this again and narrowed it down to 2 cases:   Case 1: The vertex $v$ in question has $deg(v)\ge2$. $v$ then loses its neighbours as the algorithm is applied repeatedly until $v$ becomes a leaf itseelf. At this point, $v$ is attached to another neighbour, leaving an edge. This means the algorithm can no longer be applied and we have obtained the final Prüfer Encoding for the tree $T$.  Case 2: The vertex $v$ has $deg(v)\ge 2$. It loses its neighbours as the algorithm is applied repeatedly but is deleted itself at some point in the process.   Have I gone about this wrong?  Thank you. How do you use a variable in a regular expression? I would like to create a String.replaceAll() method in JavaScript and I'm thinking that using a regex would be most terse way to do it.  However, I can't figure out how to pass a variable in to a regex.  I can do this already which will replace all the instances of "B" with "A".  "ABABAB".replace(/B/g, "A");   But I want to do something like this:  String.prototype.replaceAll = function(replaceThis, withThis) {     this.replace(/replaceThis/g, withThis); };   But obviously this will only replace the text "replaceThis"...so how do I pass this variable in to my regex string? How rare are magic items and how many should I be handing out? Is it normal for focal length to change while focusing? When I change the focus distance on my Pentax 55-300mm lens, the focal length appears to change.  More specifically, the lens appears to zoom in as I focus towards the minimum focusing distance.  This is most noticeable at the 55mm end of the lens.  Is this normal? Ubuntu16.04 boots into initramfs Ubuntu doesn't boot up and it goes into initramfs. I am writing from a live CD trial session. what should I do?  I understand that the boot flow is broken and that when the files from root are going to be loaded into the ram, it does not find the files in the root directory. Please correct me if I'm wrong.  The following is the output from ashell as I input the "exit" command:  (initramfs) exit /dev/mapper/ubuntu--vg-root contains a file system with errors, check forced. Inodes that were part of a corrupted orphan linked list found.  /dev/mapper/ubuntu-vg-root: UNEXPECTED INCONSISTENCY; Run fsck MANUALLY.     (i.e., without -a or -p options)  fsck exited with status code 4. The root file system on /dev/mapper/ubuntu--vg-root requires manual fsck How to use measured step response to tune control system How does one use a measured step response to tune either a PID or convolution control scheme? Inspired by , I'm interested a more detailed explanation of how to implement a control system based on the measured step response.  I would not try to guess all the effects.  There are probably some non-obvious things going on, and you can't know all the parameters. I would measure the step response.  Find two pump settings that both result in the ball being within the measurable range within the tube.  Then have the controller suddenly switch from one setting to the other open loop.  Meanwhile measure what the ball does over time.  That is the step response.  You can take the derivative of that and get the impulse response.  From the impulse response you can predict the motion of the ball for any history of pump settings, assuming this is a linear system.  It is probably linear enough over the small range of settings to keep the ball within its normal range. You can use this as a simulation base to find the parameters for old fashioned PID control.  Or you can use the impulse response directly to do a convolution control.  You have to low pass filter the control input enough so that convolution kernel doesn't go negative unless your pump is actually reversible and can suck the ball back down.  How exactly does this work? ; I assume &quot;convolution control&quot; is the use of the pole-zero or transfer function, but don't see exactly how to get the parameters. RELATED:  * I'm looking for a word that describes a person who is extremely dismissive and unopen to ideas or comments. Dismissive  feeling or showing that something is unworthy of consideration   For example,  Tom: 'Get your table organised! It's so-' Jack: 'Shush, bring your comments somewhere else.' This or That person Today I heard a speaker use the phrase "this person", referring to the subject-person of the story they were telling, and I heard it as (that person). Between the words “this” or “that” in context with the phrase and story-tense, which should you use. Number agreement between subject and object Could humans choose to establish fibre digesting colonies in our guts? Why is my document pdf generated by pdflatex looks different from the one generated by latex+dvips+ps2pdf ? From the code below, i have tow different papers switch to the tow cited commands above :  \documentclass[10pt,a4paper]{article} \usepackage[utf8]{inputenc} \usepackage[francais]{babel} \usepackage[T1]{fontenc} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{graphicx} \usepackage{lipsum} \author{M ROUAN SERIK} \title{Article with \LaTeXe} \fontfamily{cmr} \begin{document} \maketitle \section{Titled section} \lipsum \end{document}   Here's my pdffonts for the tow pdfs : Pdflatex:    name                   type     encoding  emb sub uni object ID   ------------------------------- ---------------- --- --- --- ---------   AMTRHA+SFRM1728        Type 1    Custom   yes yes no       4  0   DPTCLU+SFRM1200        Type 1    Custom   yes yes no       5  0   JVZRKA+CMMI12          Type 1    Builtin  yes yes no       6  0   UEWNID+SFBX1440        Type 1    Custom   yes yes no       7  0   FOVERL+SFRM1000        Type 1    Custom   yes yes no       8  0     latex+dvips+ps2pdf      name                                 type              encoding         emb sub uni object ID   ------------------------------------ ----------------- ---------------- --- --- --- ---------   WVMUEH+SFRM1000                      Type 1C           WinAnsi          yes yes no        16  0   ZHRBNN+SFBX1440                      Type 1C           WinAnsi          yes yes no      14  0   IMJWCD+CMMI12                        Type 1C           Custom           yes yes no      12  0   MDMSVR+SFRM1200                      Type 1C           WinAnsi          yes yes no      10  0   TWHNMT+SFRM1728                      Type 1C           WinAnsi          yes yes no       8  0 How to cleanup deadlinks I was reading some answers about ruby and there are a lot of links to _why's sites.  and took all his sites with him.  Almost every introduction question about ruby will include at least one or two links to one of his sites. Examples:          With a bit more effort I could probably find more questions with a lot of deadlinks.  My suggestion for discussion was, what would be a good way to solve deadlinks in the answers/comments? Not every site _why created has resurfaced somewhere else, but some could be replaced by new links.  But I wanted the discussion to go beyond this specific problem of deadlinks in the ruby answers, an automatic solution would be to let the links be scanned in a batch and when found dead be replaced by a google cache or webarchive version of the page, and perhaps mark it so that the community can replace the link with an alternative? House address is not listed on Google Maps When I search for my address on Google Maps it cannot be found which means I can't order takeaway etc.  Is there a way of adding my address to Google Maps or even add a street address?  I want the address to be publicly available so others can search it. dpkg exit with error "cannot scan updates directory `/var/lib/dpkg/updates/': No such file or directory", how to fix it? Earlier, I had a problem with a package, and I (wrongly) ran this:  rm -r /var/lib/dpkg/*   See also .  Now when I try to upgrade, I get this:  E: Could not get lock /var/lib/dpkg/lock - open (11: Resource temporarily unavailable) E: Unable to lock the administration directory (/var/lib/dpkg/), is another process using it? masoud@masoud-PC:~$ sudo apt-get upgrade  E: Could not get lock /var/lib/dpkg/lock - open (11: Resource temporarily unavailable) E: Unable to lock the administration directory (/var/lib/dpkg/), is another process using it?   and when I use: sudo dpkg --configure -a   I get this:  dpkg: error: cannot scan updates directory `/var/lib/dpkg/updates/': No such file or directory     and for sudo apt-get upgrade -f get:  Reading package lists... Done Building dependency tree        Reading state information... Done Correcting dependencies... failed. The following packages have unmet dependencies:  ia32-libs : Depends: ia32-libs-multiarch but it is not installable  wine1.4 : Depends: wine1.4-i386 (= 1.4.1-0ubuntu5) but it is not installable E: Error, pkgProblemResolver::Resolve generated breaks, this may be caused by held packages. E: Unable to correct dependencies Calculating the longest distance within polygon in QGIS I want to calculate the "diameter" of polygons in QGIS.  The "diameter" defined as the distance between the two most distant points of the polygon.  I couldn't find a fitting solution in the field calculator. Maybe you have some ideas? SELECT GETDATE()   Returns: 2008-09-22 15:24:13.790  I want that date part without the time part: 2008-09-22 00:00:00.000  How can I get that? I'm setting up a child theme in WordPress and I can't make add_action to be fired within functions.php.  Functions.php is called and I can run code from within. Any idea on what I'm doing wrong?  $debug_msg = "Hi there!";  function test_function() {     error_log($debug_msg, 0);  } add_action('init', 'test_function', 20); Does the speed of light vary in non-inertial frames? I'm trying to prove that if there are to numbers $n,m$ (natural numbers), and their smallest common multiple is $k$, so that $k = n·i$ and $k = m·j$ for some $i,j$ natural numbers, any common multiple $q$ of $n,m$ is a multiple of $k$, so that there exists a $g$ so that $q=k·g$.  Logically it seems correct, but I can't seem to prove it... Any help? change environment of a running process How might it be possible to alter some variable in the env of an already running process, for example through /proc/PID/environ? That "file" is read-only.  Need to change or unset the DISPLAY variable of a long-running batch job without killing it.