$X_1,X_2$ distributed $U(0,1)$ and independent, find the distribution of $D=|X_2-X_1|$
CDF of absolute value of difference in random variables
How can I have a different input method for each app window on windows 8. When I change input language to ENG all app window also uses this method and I don't want that. Like windows 7 that has a different input method for this purpose. thanks Why are some faces in my mesh darker? Can a creature's sacrifice benefit be taken when it is sacrificed to Eldrazi Monument? Evolutionary chronology - if any, which species have evolved in the last 100 years I heared somewhere, I cannot remember where, that there has not been an evolution observed in our lifetime. In life science class, right at the start, we was doing the usual MRSGREN (how to tell if something is a living organism), and the tutor said that you can also tell something is a living organism if it evolves. So I asked if there has been an observed evolution in our lifetime. She said that there had been many but could not recite any off the top of her head, so the next week she handed me a piece of paper with 8 or so websites that aparrently corroborated her claim. I have not got the paper anymore but I recall there been on there the peppered moth or something. So I set out to look for a chronological list of evolution but could not find an authoritative one. I could only find something on wikipedia that indicated that species have been dying out for the past thousand years, but nothing saying that any have evolved. 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? GRUB2 does not show Windows 8 option to boot into after Dual Boot Yesterday, I tried to dualboot Ubuntu 16.04 onto my hard drive, creating a new partition for Ubuntu alongside my existing Windows 8. First, I disabled the fast-boot option in Windows 8, and still GRUB did not load, and it went directly to Windows boot-up. Then I did some research and found this article:     Basically, I issued the BCDEdit command in Windows, and entered in the following code:  bcdedit /set {bootmgr} path \EFI\ubuntu\grubx64.efi   When I reboot, I get a basic GRUB2 terminal, and after I type in the exit command, then a second Shell prompt appears, and after typing the exit command again, the GRUB2 menu to select the OS to boot finally appears... with only Ubuntu and Ubuntu memory test as options, not Windows 8.  After booting into Ubuntu, I tried to run the Boot-repair Utility, but that shows this following error:   How do I approach this problem? The Pastebin log is here:   Thanks for the help! What is polarisation, spin, helicity, chirality and parity? Polarisation, spin, helicity, chirality and parity keep confusing me. They seem to be related, but exactly how they are related is unclear to me. Can someone maybe give a short overview about what these quantities mean and how they are related? What are the values for e.g. basic particles like electron or photon? My dev team is getting ready to start a new project. The shop has been a "VB shop" since the days of VB3, but the prevailing opinion now is that we're a ".NET shop" and since C# was created specifically for .NET, whereas VB.NET was a retrofit, we've decided to move forward writing C# only. The controversy revolves around the question of whether the Microsoft.VisualBasic namespace has a legitimate place in new development or if it is only for backward compatibility for VB6 (and older) code. A further, and more interesting question is whether the code "under" the Microsoft.VisualBasic namespace is even .NET code of if it is really the old VB runtime carefully packaged in a .NET wrapper, making it in fact a COM interop control (similar to how WinForms wraps the non-.NET Win32 windowing API but exposes only .NET APIs for consumption).  To make this even more confusing, our dev team has a Microsoft Consulting Services consultant telling us Microsoft no longer supports Visual Basic, including the VB runtime underlying the Microsoft.VisualBasic namespace.  What I'm looking for are links -- preferably to unimpeachable Microsoft sources -- to documentation that definitively answers this question one way or the other. I've already tried several search permutations on Google and not gotten any closer to getting to the bottom of this question.  EDIT: Apparently I didn't make my question clear. I'm not asking if VB.NET is true .NET code. I'm trying to determine if whatever is "under" the Microsoft.VisualBasic namespace is .NET code or if it's the old VB6 runtime carefully packaged and exposed as .NET code. Someone already said that 9/10 of the namespace simply wraps code from elsewhere in .NET; what about that other 1/10? Sum of independent Gamma distributions is a Gamma distribution If $X\sim \Gamma(a_1,b)$ and $Y \sim \Gamma(a_2,b)$, I need to prove $X+Y\sim\Gamma(a_1+a_2,b)$ if $X$ and $Y$ are independent. I am trying to apply formula for independence integral and just trying to multiply the gamma function but stuck ? How do I make the Unity Launcher background transparent? I found a way to make the icon backgrounds transparent for the Unity Launcher by changing the files under /usr/share/unity/4.  Does anyone know how to make the background transparent for the launcher itself? I already made it transparent under Compiz, but I want to remove the line that separates the launcher from the desktop. If anything, I just want to make it look like the icons are floating. Midpoint-Convex and Continuous Implies Convex Given that $$f\left(\frac{x+y}{2}\right)\leqslant \frac{f(x)+f(y)}{2}~,$$ how can I show that $f$ is convex. Thanks.      Edit: I'm sorry for all the confusion. $f$ is assumed to be continuous on an interval $(a,b)$. Number of Pairs of Subsets Find the number of Pairs $(A,B)$ of subsets of $[n]$ such that $A ⊆ B$? I just need clarification in my thought process. My professor's wording at times can through me off. I just want to know if I am on the right track. We will have $3$ regions: 1.Outside $B$ 2.Inside $A$ 3. Inside $B$, Outside $A$ I believe the number of pairs is $3^n$ but I am not sure. Any help would be appreciated. A variation on the induced topology (subspace topology) Is there a way to get reverse numbering on the enumerate environment? To build a list of publications, I wish to show the most recent on top of the list, while keeping the numbering similar. This can be achieved manually by doing something like:  \begin{enumerate} \item[42] pub num 42 \item[41] pub num 41 \item[...] \item[1] pub num 1 \end{enumerate}   but is there a more principled approach? Android : Is there any alternative to listFile function (Android java.io.File.listFiles()) Helvetica font has jagged edges I use 'Helvetica' as my font and build my document using Texmaker. But the PDF generated has jagged edges while using this font and when I use a different font (say Times or even Helvetica sans-serif) it builds just fine.     Please suggest if there is anyway I can get over this. The problem with these jagged edges is that it appears very dull and unreadable at 100% resolution.  OK guys, now here is the MWE  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% HEADER %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \documentclass[a4paper,twoside,12pt]{book}  %% Language %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \usepackage[T1]{fontenc} \usepackage[latin1]{inputenc} %\usepackage[utf8]{inputenc} \usepackage{graphicx,color,subfigure}  %% Line Spacing %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \usepackage{setspace} %\singlespacing        %% 1-spacing (default) %\onehalfspacing       %% 1,5-spacing \doublespacing        %% 2-spacing  %% Other Packages %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \usepackage[left=1.5in, right=1.5in, top=1in, bottom=1in, includefoot, headheight=13.6pt]{geometry} \usepackage[pagebackref=true,breaklinks=true,letterpaper=true,colorlinks,bookmarks=false]{hyperref} \usepackage{helvet} \usepackage[square,numbers]{natbib} \usepackage{hyphenat} \usepackage{fancyhdr}   \begin{document}  \pagestyle{empty} %No headings for the first pages.  \cleardoublepage %The first chapter should start on an odd page.  \pagestyle{plain} %Now display headings: headings / fancy / ...  \pagebreak  %------------------------------------------------------------------------ \chapter{Divorce}   A major change that has occurred in the Western family is an increased incidence in divorce. Whereas in the past, divorce was a relatively rare occurrence, in recent times it has become quite commonplace. This change is borne out clearly in census figures. For example thirty years ago in Australia, only one marriage in ten ended in divorce; nowadays the figure is more than one in three (Australian Bureau of Statistics, 1996: p.45). A consequence of this change has been a substantial increase in the number of single parent families and the attendant problems that this brings (Kilmartin, 1997).   \end{document} I have to prove that a function $f:]0,1] \rightarrow \Bbb R$ : $$ f(x) = \begin{cases} \frac1q,  &amp; \text{if $x \in \Bbb Q$  with $ x=\frac{p}q$ for $p,q \in \Bbb N$ coprime} \\ 0, &amp; \text{if $x \notin \Bbb Q $} \end{cases} $$  is discontinuous in every point $x \in \ ]0,1] \cap\Bbb Q$.  And then to consider $x \in \ ]0,1] \backslash \Bbb Q$ and prove that it is continuous.  For now I learned different ways to prove continuity (epsilon-delta, sequences), but I'm never sure what would be better to use in each different case.  I wanted to prove the discontinuity by using sequences: $$\forall x_n \quad x_n\rightarrow a \quad \Rightarrow \quad f(x_n) \rightarrow f(a)$$  I tried creating a sequence $ x_n=\frac1n + a$, we know it converges to $a$ but $f(x_n)\ $ doesn't  converges to $\ f(a)$ because there would still be some points not in our set (irrational numbers that creates gaps).  But I don't think it works, so I'm asking you if you could help me solving the two questions. Calculate work done by a hovering helicopter over time This is likely to be very simple, but...  How does one calculate work done by a hovering unmoving aircraft over time?  As in work in Joules.  In this scenario, to remain hovering the aircraft has to exert a force that counters gravity (which would be its mass times G, pointing in opposite direction of gravitational pull).  However, work is defined as newton per meter, and the aircraft does not move.  Meanwhile the battery charge or fuel is going to be expended, so the energy is spent.  The other question here:   is dealing with conservation energy and not calculating drain/work performed by hovering. Determine all functions satisfying $f(x + f(x + y)) + f(xy) = x + f(x + y) +yf(x)$ How to convert an instance of std::string to lower case I want to convert a std::string to lowercase. I am aware of the function tolower(). However, in the past I have had issues with this function and it is hardly ideal anyway as using it with a std::string would require iterating over each character. Is there an alternative which works 100% of the time?