How to perform Hypothesis Testing (2 samples) when one sample is normal and the other is non-normal?
Testing for significance between means, having one normal distributed sample and one non normal distributed
To show that ${x_n}$ is convergent where $|x_{n+1} - x_n|< \frac{1}{n^2}$ Let ${x_n}$ be a sequence in $R$ such that $|x_{n+1} - x_n|&lt; \frac{1}{n^2}$ for all $n \in N$.  Show that the sequence is convergent.  If it were $|x_{n+1} - x_n|= \frac{1}{n^2}$, could take help of the fact $\sum \frac{1}{n^2}$ is convergent and of triangular inequality.  But what to do here? Please help. Thanks in advance. so I am creating a few posts about bearings and wheels, (story so far):      I have now got the wheels, bearings and freehub working.  Started riding to work this morning and I almost couldn't stop at a junction.  Thankfully wasn't going too fast.  I physically can not get the wheel to lock.  I have to use both brakes at full force to get the bike to roll to a stop.  If I only use one brake I would not stop at any junction in time.  Could the cause be any of the following:   Over greased bearings? Over greased axle? not tightened cone hubs enough? not tighted axle enough?   I do not have any grease on the disk brakes them selves.  Rather nervous getting on the bike now.  Don't seem to be doing too well with this bike home fixing thing.  over greased bearings?  EDIT  Forgot to mention that it is hydraulic disk brakes.  EDIT 2  So in the end I took it to the LBS as I didn't have much confidence in my self at this point.  They had to replace the front pads but where able to clean the rear and cleaned the rotors.  (I had tried to clean the rotors but obviously not vigorously enough).  He said it was a bit of a pain to do.  All is working again.  They double checked my wheels and said I had put them back together correctly which is reassuring.  Thanks for all the help Place label in middle of line with TikZ What is the best way to place a label in the middle of a line with TikZ? I mean smack dab in the middle of the line, not above or below it. The following is close  \begin{tikzpicture} \draw[|-&gt;, color=red] (-4cm, 0.5cm) -- (2.5cm, 0.5cm) node[midway, color=black] {$\tau_{r}$}; \end{tikzpicture}   But the line crosses right through the node and its text, which is bad.  I don't know if there is an option to choose the background color of a node, which I think would solve the problem (e.g. background=white). fill doesn't seem to work. Ubuntu 16.04.1 has appeared as .rar file. How do I burn it to a disk to use to install Ubuntu? I am interested in using Ubuntu for the fist time, so I went to the Ubuntu download page (), to get the download file. When the file downloaded he file, it appeared in WinRAR, so I cannot burn the file to a DVD. Can anybody point me in the right direction as to how to burn this file to a DVD when the file appears as a WinRAR file? Any help would be great appreciated. Thanks :) Extracting Windows 8 Start Screen Patterns Is there any way to extract the Windows 8 Start Screen patterns, in order to use them as standalone wallpapers on other systems?  For example see this screenshot:    I am interested in the dark blue background. I heard that this background is somehow adapted to your chosen color theme. So many different variations should exist.  Engadget has an article  briefly talking about these background patterns and the different color schemes. They call them "personalization tattoos".    Update:    I found the following page/guide:   This looks a very good way to achieve my goal. Unfortunately the guide seems to be dated.  I tried to find shsxs.dll on the RTM of Windows 8 without much luck. It looks like Microsoft changed the way they handle the background image. The file is nowhere to be found...  I also looked into uxtheme.dll, but it doesn't contain any interesting images.  Any new ideas? Any other *.dll with might be of interest here? I have used so many things like url removal request and deleted the pages etc., but still the errors are shown in my webmaster tools.  How can I remove the urls completely from Google? Given that $\displaystyle{a+b\sqrt[3]{2} +c\sqrt[3]{4} =0}$, where $a,b,c$ are integers. Show $a=b=c=0$  Do I use modular arithmetic? Making SSD & HDD work together like a hybrid Can open, unsafe nuclear fusion reaction burn the atmosphere? I happened to hear people saying that the nuclear fusion bomb tests could set the atmosphere on fire. I have some serious doubts about that - but I have no facts. Nuclear fusion reaction requires $15*10^{6}$ kelvins to start. If we produce such temperature in "open air" would the atmosphere become a fuel for further fusion? Shouldn't the whole thing just be torn apart by its terrible pressure? get emacs to automatically use biber instead of bibtex I was reading the question titled .  In that question, user @PLK mentions that as of auctex 11.87, auctex should automatically check if you are using biblatex and if so, switch to using biber.  I have auctex 11.87 installed and running, but I am not getting this automatic switching behavior.    Say I have two files (borrowed from ).  test.tex  \documentclass{article} \usepackage[backend=biber]{biblatex}  \addbibresource{test.bib} \defbibheading{bibliography}{}  \begin{document}     \nocite{*}     \subsection*{Journal Publications:}     \printbibliography[type=article]      \subsection*{Conference Publications:}     \printbibliography[type=inproceedings]  \end{document}   and test.bib  @ARTICLE{abc,   author = {A Author},   title = {the article title},   journal = {the journal},   year = {2012},   volume = {1},   pages = {1--2},   number = {1},   month = {1},   doi = {1234/5678} }  @INPROCEEDINGS{def,   author = {A Author},   title = {the proceeding title},   journal = {the conference},   year = {2012},   volume = {1},   pages = {11--12},   number = {1},   month = {1},   doi = {5678/1234} }   If I run the following commands:  pdflatex test.tex biber test pdflatex test.tex   I end up with a properly processed document.  In emacs, when I press C-c C-c and select the BibTeX command, emacs runs bibtex test instead of biber test.  I am then greeted with errors about no \citation \bibdata or \bibstyle commands.  My bibtex-dialect variable is automatically getting set to biblatex, LaTeX-biblatex-use-Biber is set to t, TeX-command-Biber is set to Biber, but for some reason TeX-command-BibTex variable is still set to BibTeX.  Should this automatically get changed to Biber?  Do I have to set it using a local variable?  Is this a bug, or am I doing something wrong?  EDIT  According to  in the AUCTeX 11.87 manual:      In case you use biblatex in a document, AUCTeX switches from BibTeX to Biber for bibliography processing.   So I feel like this automatic switch should already be happening. Variance (different definitions) I'm new to statistics and reading stats books I found different definitions for Variance.  Definition1: $ s^2 = \frac{1}{n-1} \sum_{i=1}^n (x_i - \bar{x})^2 $  Definition2: $ s^2 = \frac{1}{n} \sum_{i=1}^n (x_i - \bar{x})^2 $  I would like to know why is used different definition for same thing? Do there exist an infinite number of integer-solutions $(x,y,z)$ of $x^x\cdot y^y=z^z$ where $1\lt x\le y$? Question : Do there exist an infinite number of integer-solutions $(x,y,z)$ of $x^x\cdot y^y=z^z$ where $1\lt x\le y$ ?  Motivation : After struggling to find a solution, I've just got one solution, which is  $$(x,y,z)=(1679616, 2985984, 4478976).$$  In the following, I'm going to write how I got this solution.  Letting $d$ be the greatest common divisor of $x,y,z$, we can represent $$x=ad, y=bd, z=cd$$ where $a,b,c$ are coprimes with each other. Then, we get $$d^{a+b-c}\cdot a^a\cdot b^b=c^c.$$  In the following, let's consider without the condition $x\le y$. Here, I suppose  $$a=2^m, b=3^n, a+b-c=1.$$  (As a result, this supposition works.)  Then, we get $$d=\frac{c^c}{2^{ma}\cdot 3^{nb}}.$$  Hence, letting $c=2^k\cdot 3^l$, if  $$kc\ge ma=m\cdot 2^m, lc\ge nb=n\cdot 3^n,$$ then $d$ is an integer.  Since $(m,n)=(4,2)$ satisfies the above conditions, then we get $d=2^8\cdot 3^6=186624.$ Hence we can get  $$x=9d=2^8\cdot 3^8=1679616, y=16d=2^{12}\cdot 3^6=2985984, z=24d=2^{11}\cdot 3^7=4478976.$$ Note that here I interchanged $x$ and $y$.  P.S : I was surprised to get this solution because I got this almost by chance. So, I don't know the other solutions. If you have any helpful information, please teach me. Can we some how use color labels on icons like OS X?  Something like this: Using vim with latex suite on two different computers, on one it's fine, but on the other my tikz pictures ''colapses'' (all text is put to the center of the figure, nothing is drawn) The same pc can compile fine from texstudio, but not from vim- latex suite  Edit: Seems the problem was compiling to dvi instead of pdf Center of a group ring? Let $R$ be a ring with unity and let $G$ be a group. Then what is the center of the group ring $R(G)$? I feel that the center $Z(R(G))$ is $R(Z(G))$. I assumed if $x=\sum_{i=1}^{n} r_i g_i$, then it should commute with every element of $R(G)$. In particular it should commute with $g=1 \cdot g \in R(G)$ Thus we get $$\big(\sum_{i=1}^{n} r_i g_i\big)g=g\big(\sum_{i=1}^{n} r_i g_i\big)$$ Thus I get $$g_i \cdot g=g_i \cdot g \text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ } \forall g \in G$$ Hence $x \in Z(R(G)) $. Is this correct? What is the best way to restore the state of ViewController how to avoid number repeation by using random class in c#? How strong is Superman on Krypton? When Superman goes back to visit his home planet (using his ability to travel through time, I guess), is he:    an exceptionally strong and athletic Kryptonian? just an average Kryptonian male? a weakling on account of spending a lifetime in the comparative microgravity of Earth?   A possibly related question: why is Superman so muscular? What kind of weights does he lift to stay in shape?  The answers to  are all about Superman's superpowers on Earth compared with other visitors from Krypton; I'm asking about Kal El without his superpowers.  Clarification: I'm asking about the "classic"  Superman, say late Golden to early Silver Age, roughly 1945-1960. (Yes, I know the concept evolved during those years.) I'm not sure what that would be in terms of "numbered Earths", those came along after my time. I'm pretty sure the Kryptonians of that era had no superpowers in their native milieu, nor would Kal El if he were deported in space-time to his native world. Can I configure it to allow:   select right-click to copy right-click or ctrl-v to paste? I have a solid understanding of most OOP theory but the one thing that confuses me a lot is virtual destructors. I thought that the destructor always gets called no matter what and for every object in the chain. When are you meant to make them virtual and why?