My current idea is the following: practically we want to get the distribution of the sum of $n$-times of a discrete uniform distribution between $1,...,m$ .  It is practically the discrete convolution of these, which is a multiplication in the space of the Laplace/Fourier/$z$-transformations. Going in this direction I found complicated formulas whose de-transformation was already hopeless. (I could write them here on need.)  Was it a good direction? Maybe somebody knows the formula, or can show me a better way?
Assume the dice are numbered from $1$ to $k$. My hunch is that this will form a normal distribution with a median at $n\cdot\frac{k}{2}$. However, I have no idea as to    turn this fact into an answer (I have a minimal knowledge of stats, but I know that I am missing the standard distribution) and this is probably the wrong approach   How can I approach and solve this problem? (Aside, this is not for a class, stats or other, so any and all approaches welcome).  *Edit: * I want to find the number of ways that the sum of the numbers that are rolled has a particular value, if $n$ dice are rolled, and each has $k$ sides, numbered $1$ to $k$.
Find the maximum value of $ f(x) = \int^{x}_{0} \sqrt{(x^2-x)^2+y^4}~dy$ Find the maximum value of $f(x)$ when $0 \leq x \leq 1$ and $$ f(x) = \int^{x}_{0} \sqrt{(x^2-x)^2+y^4}~dy$$   I'm guessing that the Fundamental Theorem of Calculus can't be used because the integrand is a function of $x$.  Any help would be greatly appreciated. What is the difference between "gerund" and "infinitive"? What is the difference between "gerund" and "infinitive"? I do not understand the differences.Can you explain them? Set the size of pgf picture? I have a pgf picture which I insert with:  \input{m1.pgf}   But the image is too big. Instead of regenerating a smaller image, I'd rather take advantage of vector graphics, and have XeLaTeX scale it. How do I set the width of pgf picture (keeping its aspect ratio)?  MWE  tex:  \documentclass{article}  \usepackage{fontspec} % enagles loading of OpenType fonts \usepackage{polyglossia} % support for languages  % fonts: \defaultfontfeatures{Scale=MatchLowercase,Mapping=tex-text} % without this XeLaTeX won't turn "--" into dashes \setmainfont{DejaVu Sans} \setsansfont{DejaVu Sans} \setmonofont{DejaVu Sans Mono}  % pgf: \usepackage{pgf}  \begin{document}  \input{m1.pgf}  \end{document}   Sample pgf:  (it's too big to cite it here, and I can't make much smaller). Jquery, changing background image with timer Maybe I'm searching for the wrong thing, but I can't see how I can do this.  I have two servers:   Server A (has SQL Server 2012 installed) Server B (has SQL Server 2014 installed)   Server A provides an API via IIS. The code both inserts and gets data from the database depending on the API call.  Server B does exactly the same for its local database.  I would like to have it so that the two databases are consistent copies of each other. I do believe this is what HA accomplishes.   So a load balancer, for example, might direct API calls to A sometimes, and B sometimes, but the data needs to be consistent either way.  I found some documentation on HA for SQL Server 2012, but not on how to do this for a mixed environment of 2012 and 2014.  Any help or pointers to documentation would be great! Thanks. I need to include a couple of Python code listings, where the indentation of the lines (using some number of spaces) is significant. I would like for the code listings to be copyable, so the spaces at the beginning of the line need to be be copied along with the text.  This question has been asked in various ways before (e.g. , or ). Those questions focus on making line numbers uncopyable, though.  Making the spaces at the beginning of a line copyable seems to be harder: "I am not sure it is possible to specify in the PDF (at least in a viewer-independent way) that the indentation should be copied too" (). At , Philippe Goutet suggests a solution (turning the spaces into visible spaces, and coloring them in the background color so that they appear invisible) that works using Acrobat Reader, but not all readers. He says "It works under Acrobat Reader and it's extremely pleasant to be able to quickly copy/paste code without problem (perhaps the problem can be circumvented by writing direct PDF code to tell that it's a space, I've never had the time to try)".  Is it possible to produce a PDF with a code listing with copyable real spaces at the beginning of a line?  Minimal example: The line return x should start with four spaces.  \documentclass{article}  \begin{document} \begin{verbatim} def myfunction(x):     return x \end{verbatim} \end{document}   I know that I could attach the code to the PDF as a file, but that's not what I want. How to specify ec2 instance types for different services? After I have specified a default EC2 instance type for my Juju charm, how do I override that for one of the services?  For instance, the  deploys wordpress and mysql, and I can set the default-instance-type in my environments.yaml so both services are m1.small  But how do I configure it so that (only) the mysql service gets deployed on an instance type better suited to a database, like m2.xlarge ? I have written a small script to count number of occurrences of logs in a particular file. The following is my code:   #!/bin/sh count=1 while read line do     found=$( grep M $line )     OCCURENCE=$( grep M /log.txt)     if [ "$OCCURENCE" ]; then         echo $count")" $line &gt;&gt; filesave.txt     fi     count=$((count+1)) done &lt; log1.txt   but I am getting this error:  ./count.sh ./count.sh: syntax error at line 10: `found=$' unexpected I have read that a holomorphic function in an open disc has a primitive in that disc. Does this mean that for any holomorphic function $f$ in any open set $U,$ that $f$ has a primitive? I say this because I can take a large enough open disc to cover the open set $U$ and find its primitive there. Is this a correct way of thinking? Testing convergence of series $\sum_{n=3}^\infty\frac{1}{n (\ln(n))^p(\ln\ln(n))^q}$ Lets have this problem. $$\sum_{n=3}^\infty\frac{1}{n (\ln(n))^p(\ln\ln(n))^q}$$ I have rewritten this to a form $$\sum\frac{1}{np'^{\ln\ln(n)}q'^{\ln\ln\ln(n)}}$$ For $p,q\in\mathbb{R}$. Obviously, $p',q'&gt;0, p=\ln(p'),q=\ln(q')$ I have been trying to add some boarding passes to wallet. I have downloaded the airline app and logged in. I have tried to "scan the code" as suggested in wallet, but the only code is a QR code and nothing happens when I try to scan. This should be that difficult but I cannot figure it out. Is there an easy way to get this done? Please explain to me how to do it. Thanks. Password protect folder without disk images? Is this possible? I know you can protect a .dmg file, but is there a more convenient solution, by using a third party application? I've heard that you need to get a Mac if you want to develop iPhone apps. Is this true?   Is it possible to develop iPhone apps using Linux? If yes, what do I need and where do I download the necessary tools? Are IP addresses with and without leading zeroes the same? Processor: PIC18F66K22 Compiler:  C18 (XC8 is fine also)   I've just made (and succesfully tested) code to measure the voltage on AN4 analog pin.  Now I want to try something else, not quite sure if it's theoretically possible.  My test-board has a PIC processor, with VDD,AVVD connected to a supply (ranging from 0(if the battery is empty/disconnected) to 4,2(full battery).  Can I use ADC to measure the VDD(-in) of my board?  Why not?:   It's not an ANx pin, not sure how to make the ADC measure it? (Channel?) If the voltage on VDD(-in) drops, will my ADC reference voltage also drop? (So when my PIC only gets 3,3V the ADC will still say it's 100% (as the max Voltage on the chip, also the reference is 3,3V).   Why/what do you ask?:   Can I just measure Channel 30 (VDDCORE)? Could I set my Vref to Vdd and measure a precision voltage reference with the A/D converter. (Not sure how) Or I could add a wire from VDD-in to an ANx pin? Will Internal VREF+ (4.096V) stay 4+V when the VDD-in is around 3,4V? Is there some kind of transformator that makes it so? Internal VREF+ (4.096V) is a bit lower than the max of the battery (4,2V), does this mean I can damage the ADC? Or just that the result will be max when the battery is full. (4,2V out of 4,096V)     Please mind that my knowledge of Electronics is "low". I've learnt way more about the software part in my education, but I'd like to know more about (Embedded) Electronics as it's a crucial part in Embedded Engineering. (It's sad how my school doesn't see this.) Merging two incoming broadband lines for faster Internet We have a broadband line coming into our building which delivers around 8-10Mbps, which is okay but not great. Fiber is available in our area (30-100Mbps) but it's not available where we are just yet.   Is there some way we could connect two lines (which we would take from two different providers so we would have redundancy if one failed) and merge them into one signal which we could distribute?  Is there some sort of setup that can do this?  Of course we have the option of a leased line but for 12Mbps symmetrical upload/download we'd be looking at around £500 per month compared to £15 per month for normal or fiber broadband.  I made a small pseudo flow chat of the setup below: If granted omniscience and we know that $\beta_1$ in a multiple linear regression model is truly 0, what does that mean in words (and math notation)?  The model is: $Y = \beta_0 + \beta_1X_1 + \beta_2X_2 + \epsilon$  Does $\beta_1 = 0$ mean:   Empirically: "If we make infinite, perfect measurements of our data, $\hat\beta_1$ approaches 0 at the limit?" [Math: ??] Formally: "In the true, finite population of our data, $X_1$ has 0 association with $Y$ and their vectors of values are perfectly linearly independent, uncorrelated, and orthogonal?" [Math: ??]   What does $\beta_1 = 0$ mean, precisely? What's the best way to use SOAP with Ruby? A client of mine has asked me to integrate a 3rd party API into their Rails app.  The only problem is that the API uses SOAP.  Ruby has basically dropped SOAP in favor of REST.  They provide a Java adapter that apparently works with the Java-Ruby bridge, but we'd like to keep it all in Ruby, if possible.  I looked into soap4r, but it seems to have a slightly bad reputation.  So what's the best way to integrate SOAP calls into a Rails app? Change \headheight for a \pagestyle I have a document class that auto generates header from some user input. The problem is the first page should have a different page header than the others and the headline can be multi line. So \headheight is too small. Here is a demonstration of the problem:  \documentclass[twoside]{scrartcl} \newcommand{\longfirstpagehead}{% \begin{minipage}{10cm} some\\long\\text\\text\\text\\text\\text\\text \end{minipage}} \newcommand{\normalhead}{normal} \usepackage{scrpage2}  \newpagestyle{firstpage}{%     {\longfirstpagehead\hfill} %twoside links     {\longfirstpagehead\hfill} %twoside rechts     {\longfirstpagehead\hfill} %oneside     (\textwidth,1pt) }{%     {\pagemark\hfill} %twoside links     {\hfill\pagemark} %twoside rechts     {\hfill\pagemark} %oneside } %  \newpagestyle{normal}{%     {\normalhead\hfill} %twoside links     {\normalhead\hfill} %twoside rechts     {\normalhead\hfill} %oneside     (\textwidth,1pt) }{%     {\pagemark\hfill} %twoside links     {\hfill\pagemark} %twoside rechts     {\hfill\pagemark} %oneside } %    \pagestyle{normal} \AtBeginDocument{     \thispagestyle{firstpage}}  \usepackage{blindtext} \begin{document}     %\vspace*{1cm}     \blindtext      \blindtext     \pagebreak \end{document}   I tried to read the height with \settototalheight and:   add a \vspace at beginning of document (unnice hack):  still the bad box warning (of cause) first section has different alignment  manually change \headheight in pagestyle  text height and page foot is wrong (can't change this because some scoping?)  use Komascript in pagestyle  \recalctypearea warning  geometry in pagestyle  pretty much the same problem like the manual attemp    So I would like to change the \headheight for the pagestyle firstpage, but the page should still have the same page margins, etc. The problem is that this has to work with \thispagestyle. (Better Ideas are also welcome) Something like \thispagegeometry in geometry would be great. ;) Stack Exchange doesn't know when I last checked my global inbox? I am subscribed to get my unread inbox items every 3 hours. It's working well, but today I noticed something quite weird:    For sake of future search, adding the text:  The following item was added to your Stack Exchange global inbox since you last checked it on 2015-05-18  But that's just not true, I checked my inbox yesterday. Not 7 months ago. Can it be fixed, or did I miss something? Even going to my  did not &quot;fix&quot; this, got today another email with the same date as yesterday.