true story about probability?
More examples of Simpson's Paradox, barring the ones on Wikipedia, Titanic, and delayed flights.
I'm having issues with my macbook pro OS X 10.7.5.  It used to connect to the wifi router (D-Link N300, DIR=615) no problems.  But for the past several weeks, I haven't been able to at all.  What pops up when I select my wifi network from the list:   "Failed to join "network" A connection timeout occured".   What happens when I try to enter my password manually:   "Connection timeout"   What I've tried to do as solutions:   Google Restart router by pressing reset &amp; refresh button Delete System &amp; User (Login) Keychain access Network > Gear symbol by the + and - bottom left of the screen > Set Service Order > Drag Wifi to the top Faithful group actions for singleton group or for empty set Let $G$ be a group, possibly a singleton. Let $M$ be a set, possibly empty. Let $\mu: M \times G \to M$ be a right group action. Let $1_G$ be the identity of $G$.  I understand 's second definition of faithful as follows:     $\mu$ is faithful if for each $g \in G$ such that $g \ne 1_G$, there exists $x \in M$ such that $\mu(x,g) \ne x$. $\tag{1}$   Later  says if $\mu$ is free and $M$ is a non-empty set, then $\mu$ is faithful.  Question: Given the idea that we can have $M$ as an empty set, I would like to clarify: Are these correct?   If $G$ is a singleton, then every action $\mu$ is faithful, whether or not $M$ is empty. If $G$ is not a singleton, but $M$ is empty, then every action $\mu$ is not faithful. Adding a comment should not make me fail the review audit Is a URL allowed to contain a space? Is a URI (specifically an HTTP URL) allowed to contain one or more space characters? If a URL must be encoded, is + just a commonly followed convention, or a legitimate alternative?    In particular, can someone point to an RFC that indicates that a URL with a space must be encoded?  Motivation for question: While beta-testing a web site, I noted that some URLs were constructed with spaces in them. Firefox seemed to do the right thing, which surprised me! But I wanted to be able to point the developers to an RFC so that they would feel the need to fix those URLs. If a motherboard doesn't explicitly support a RAM frequency, is still compatible? For example, my  says this:   Supports DDR3 2133(OC)/1866(OC)/1600/1333/1066 non-ECC, un-buffered memory   Is RAM clocked at 2400 MHz compatible? Will the performance be downgraded or it just won't work?  I found other questions but they were related to the CPU cap at 1600 MHz. This cap is related to the motherboard, specs says 2133(OC) max. Let $\ln X \sim \operatorname{Exp}(1)$ and $X,Y$ i.i.d.  What is the distribution of $Z=XY$?  My attempt: $$P(Z\le z)=P(XY\le z)=P(\ln(XY)\le \ln(z))=P(\ln(X)+\ln(Y)\le \ln(z))$$  We need the convolution, since $\ln X $ and $\ln Y$ are independent we get, $$\int_0^{\ln(z)} f_{\ln(X)}\circledast f_{\ln(Y)}=\int_0^{\ln(z)}e^{-y}e^{-x+y}\,dy=e^{-x}ln(z),$$ i.e. $e^{-x}\ln(z)$ is the density of $XY$ Why does space expansion not expand matter? I have looked at other questions on this site (e.g. "why does space expansion affect matter") but can't find the answer I am looking for.  So here is my question: One often hears talk of space expanding when we talk about the speed of galaxies relative to ours. Why, if space is expanding, does matter not also expand? If a circle is drawn on balloon (2d plane), and the balloon expands, then the circle also expands. If matter is an object with 3 spatial dimensions, then when those 3 dimensions expand, so should the object.  If that was the case, we wouldn't see the universe as expanding at all, because we would be expanding (spatially) with it.  I have a few potential answers for this, which raise their own problems:   Fundamental particles are 'point sized' objects. They cannot expand because they do not have spatial dimension to begin with. The problem with this is that while the particles would not expand, the space between them would, leading to a point where the 3 non-gravity forces would no longer hold matter together due to distance Fundamental particles are curled up in additional dimensions a la string theory. These dimensions are not expanding. Same problems as 1, with the added problem of being a bit unsatisfying. The answer seems to be (from Marek in the previous question) that the gravitational force is so much weaker than the other forces that large (macro) objects move apart, but small (micro) objects stay together. However, this simple explanation seems to imply that expansion of space is a 'force' that can be overcome by a greater one. That doesn't sound right to me. I use a lot of lists and arrays but I have yet to come across a scenario in which the array list couldn't be used just as easily as, if not easier than, the linked list.  I was hoping someone could give me some examples of when the linked list is notably better. Unable to install Ubuntu on Lenovo Y500 I am totally unable to install any flavor of Linux on my lenovo Y500. TL;DR:  with EFI on -&gt; cannot even access installer with legacy - &gt; installer runs fine, but installed OS never boots  Long Version: It is going to be hard to recap what I did, because I tried so many things, but here is the gist of it: EFI mode (secure boot disabled): Trial #1  ubuntu 12.10 x64 &amp; Mint 14 x64 boot from usb see screen with choices pick &quot;try ubuntu&quot; get black screen  Trial #2  ubuntu 12.10 x64 &amp; Mint 14 x64 boot from usb see screen with choices press &quot;e&quot; to enter edit mode remove &quot;quiet splash&quot; replace with &quot;nomodeset&quot; end up on the command line with an error message from x server: &quot;no screen found&quot; try fiddling around with xorg.conf to no avail  Trial #3  Arch Linux Live USB EFI mode no boot  Trial #4  ubuntu 12.10 x64 &amp; Mint 14 x64 set &quot;e&quot; to enter edit mode in menu add acpi=off end up with &quot;(initramfs) unable to find a medium&quot; message  Trial #5  same as above set SATA mode to legacy (it was AHCI) error loop that says something along the lines of &quot;ata1.00: hard resetting link&quot;  Legacy Mode Trial #1  ubuntu 12.10 x64 &amp; Mint 14 x64 USB boot Everything seems to work Proceed to normal install (picks SSD drive by default) Everything seems to work reboot blank screen reboot with &quot;shift&quot; pressed see message &quot;grub loading.&quot; and nothing As per advised on Ubuntu's community EFI page, run boot-repair same results run boot-repair again same results  Trial #2  ubuntu 12.10 x64 &amp; Mint 14 x64 same as above, but pick 1T HDD as target install same results  Trial #3  create a /boot partition on the SSD install on SSD same results (&quot;grub loading.&quot;) run boot repair twice same results  Trial #4  create a GPT filesystem on HDD create a /boot partition on the HDD install on HDD same results as above  Trial #5  install ubuntu on HDD install boot on all drives (HDD &amp; SSD) same results  Trials #6  install Arch on SSD no boot loader found  Notes:  Every step has been tried with multiple USBs. All isos' MD5Sums have been verified LiveUSBs have been created both through ubuntu's embedded app and unetbootin (save for Arch's live USB which was created by DDing the iso as per advised in the Arch wiki) I have wiped out windows in my first trials, and I don't care, I am never going to use it. I don't want to dual-boot. I just want Ubuntu or Mint or Arch as far as I can remember (it gets hard after 50+ trials), I tried every option with sata mode IDE or normal. Not sure though.  I've also tried numerous other things that I can't recall right now. All in all I've been giving this 3 to 5 hours a day for a week and a half to absolutely no avail. I am extremely disappointed as this is my first Lenovo and word is Lenovo is Linux-friendly...I have never spent more than an hour installing linux on any machine. What's even more frustrating is that it seems to be working for , and I can't find any hint telling me how they managed. I wrote to one guy who posted a serie of youtube videos about how to get everything working perfectly on the Y500, and he told me he just installed mint without any problems. Might be I am a particular case because I have the SLI version of the Y500. If anyone has pointers, incomplete solutions, ideas, black magic, I'll be forever in debt. Thank you P.S: This question, afaik, is not a duplicate of an existing question. I've scoured all questions containing &quot;lenovo&quot; and &quot;install&quot;, and none applies to me. I believe in Windows Vista, we could use linkd command. However, I cannot find this command in Windows 7. I know I can use Windows Explorer and delete the junction, but I wonder if this can be done in Command Prompt.  I can use mklink command to create a junction from a Command Prompt, so, what is the opposite of it (something like linkd)? My question is specifically for badges in a particular tag. I've heard that the rules have been changed.  How and when can one get bronze, silver and gold badges for a specific tag, say ? What are the new rules governing these badges? Apply brace expansion in "reverse order" Is it always better to use 'DbContext' instead of 'ObjectContext'? Below is the text in the file:  Pseudo name=Apple Code=42B state=fault  Pseudo name=Prance Code=43B state=good   I need to grep for "42B" and get the output from the above text like:   Pseudo name=Apple Code=42B state=fault   Does anyone have idea on how to achieve this using grep/awk/sed? Dynamic Comparison Operators in PHP I would like to parse a string such as p1=6&amp;p2=7&amp;p3=8 into a NameValueCollection.  What is the most elegant way of doing this when you don't have access to the Page.Request object? What is $\lim_{n\to \infty}\sum_{k=1}^n \left(\frac{k}{n}\right)^n$? I'm asked to find $\displaystyle\lim_{n\to \infty}\sum_{k=1}^n \left(\frac{k}{n}\right)^n$.  It seems that the sum converges.  I managed to prove that $\forall n,1&lt;\sum_{k=1}^n \left(\frac{k}{n}\right)^n&lt;e$  But I don't know how to prove convergence, nor find the value of the limit. It looks like if I load dynamic content using $.get(), the result is cached in browser.  Adding some random string in QueryString seems to solve this issue (I use new Date().toString()), but this feels like a hack.   Is there any other way to achieve this? Or, if unique string is the only way to achieve this, any suggestions other than new Date()? Please Join Us in Welcoming Our New Meta Stack Exchange Moderators! Logistic Regression - Adding interactions makes Independent variable statistically insignificant My name is Abhi &amp; I am trying to better understand logistic regression by solving a few practice problem. I am using R and RStudio as the development environment  Problem Statement  Given the age, sex and class(first,second,third) for each passenger can you predict if he survived or died when the titanic sank   Attempt1  Simple Logistic Regression. Use age,sex and passenger class directly. The formula (in R)  Survived~Pclass+Sex+Age  This gives fairly decent results - accuracy of 79% and all of independent variables are statistically significant   Attempt2  Add interactions between age,sex and passenger class. Accuracy has improved to 80% but age is no longer significant. Also none of the new terms(age-sex,age-class,sex-class,age-sex-class) are statistically significant. The formula (in R) Survived~Pclass*Sex*Age   Can some one explain why this is happening? I can accept that the new terms may not be significant but why is age no longer significant?   Any help would be much appreciated