I know that in general if the correlation of two random variables is zero, it is always true that two variables are independent, and it is possible to provide some examples which are dependent with zero correlation. However, all examples that I have seen, use nonlinear relation between two variables. Can we say if two random variables have zero correlation will be independent (not using nonlinear relation but linear model)?
If two variables have 0 correlation, why are they not necessarily independent? Are zero correlated variables independent under special circumstances ?  If possible, I am looking for an intuitive explanation, not a highly technical one.
Riddle (simple arithmetic problem/illusion) I'm not sure how well known this "riddle" is but here it goes.  3 people go to a restaurant, each buy food worth 10.00.  When they're done, they give 30.00 to the waitress.  She gives the money to the manager, manager says they paid too much, gives 5.00 back to the waitress.  She comes back to the table, gives a dollar back to each person and then puts the remaining 2.00 in her pocket for tip.  So now, each person has paid 9.00.  9.00 x 3 = 27.00.  Plus the 2.00 in the waitresses pocket is 29.00.  What happened to the 30th dollar?  So what's the issue with this way of calculating (since if you backward it works fine), that doesn't give us the correct result? What is the difference between a gameplay programmer and a game designer/developer? Multi-Question Questions: How Best to Handle Them? Sometimes I come across a question on SO that is actually a number of questions all in one. If these &quot;sub-questions&quot; are closely related, it's not a problem. But if they are only weakly related (or not at all) it gets ugly. I'm now (ironically or hypocritically) going to ask a few questions of my own for the community to respond to:  Do you consider a question made up of a number of weakly-related sub-questions &quot;inappropriate&quot;? Why or why not? How many is too many sub-questions? What do you think is the best way to deal with such questions?  As an example,  I had some discussion about with another user. I will add a more complete version of my response in an answer below, but in short I felt that this question should be closed and many of the questions asked separately. I'm trying to split text in a JTextArea using a regex to split the String by \n However, this does not work and I also tried by \r\n|\r|n and many other combination of regexes. Code:  public void insertUpdate(DocumentEvent e) {     String split[], docStr = null;     Document textAreaDoc = (Document)e.getDocument();      try {         docStr = textAreaDoc.getText(textAreaDoc.getStartPosition().getOffset(), textAreaDoc.getEndPosition().getOffset());     } catch (BadLocationException e1) {         // TODO Auto-generated catch block         e1.printStackTrace();     }      split = docStr.split("\\n"); } How do I fix my USB drive to get its original 8GB size back? My USB drive used to be originally 8GB when I bought it.  I'm trying to reformatted in Windows 7 by right clicking on the drive and selecting Format.... But the capacity only shows 250MB.  Is there something I can do to get the original size back? Maybe it got partitioned in a weird way?   The  flash drive is a SanDisk Cruzer Micro 8GB. I got it from Wal-Mart but this is the same drive. Complete view of where the PATH variable is set in bash Say I have two normal distributions A and B with means $\mu_A$ and $\mu_B$ and variances $\sigma_A$ and $\sigma_B$. I want to take a weighted mixture of these two distributions using weights $p$ and $q$ where $0\le p \le 1$ and $q = 1-p$. I know that the mean of this mixture would be $\mu_{AB} = (p\times\mu_A) + (q\times\mu_B)$.  What would the variance be?    A concrete example would be if I knew the parameters for the distribution of male and female height. If I had a room of people that was 60% male, I could produce the expected mean height for the whole room, but what about the variance? Undefined control sequence error on \fancy@reset, \f@ncyolh and \f@ncyorh when using newlfm class GCD of the already GCD What are "Community Wiki" posts? Some questions and answers are marked Community Wiki and are owned by a community wiki user:  (In fact, this very question is one of them)  Why have Community Wiki posts? How do Community Wiki posts work? How does a post become a Community Wiki post? How can the Community Wiki status be removed from a post? How can I find Community Wiki posts? How to tell Google to crawl distinct part of the webpage? What approach should I take to make the website Google-friendly, .  The problem is that when a specific content is being requested (eg. ) user is taken to the page using scrollbar, though the surrounding content is still being loaded. How to tell Google that for this URL  only the #36 entry should be crawled.  Is there a tag or other way to select the surrounding content as irrelevant for the URL? x tick label style issue, anchor=east and text width command not working together IndentationError: unindent does not match any outer indentation level When I compile the Python code below, I get      IndentationError: unindent does not match any outer indentation level     import sys  def Factorial(n): # Return factorial     result = 1     for i in range (1,n):         result = result * i     print "factorial is ",result     return result   Why? Using Illustrator CS6 to create shape out of multiple paths I am very new to Illustrator, in fact I am only experimenting with it in an attempt to help my friend develop a logo for a new business venture. I managed to draw out the shell of the logo using the line tool and modifying the lines with the anchor tool to get the shape I wanted.  However, I would like to somehow take all of these paths and create one object, or symbol which I can then apply a drop shadow, fill and various other effects too. Currently when I try to do this I get unwanted effects...  I'd appreciate any help on the subject. Let $p$ be a prime number and $G$ a non abelian group or order $p^3$. Prove that $Z(G) = [G,G]$.   I have already figured out that $|Z(G)| = p$, and that $G'=[G,G] \lhd G$.  Also, $|G'| = p$ or $p²$.  I suppose I'd have to prove that $G' \subset Z(G)$, but I've been trying and I have no idea how. Any hints? Thanks! If you create a scene for the Video Sequence Editor and start working on a project Blender will render the output from the VSE. But if you want to later switch it to render your 3D scene again (the camera output) where is the setting to select the source?  Usually I keep a separate .blend for VSE edits so I don't need to switch, but I feel like I ought to learn how to do this as it's pretty basic. I would expect to find this in the Render context but I see no place to specify the source.  Thanks. What does '>/dev/null 2>&1' mean in this article of crontab basics? I'm shooting with a Nikon 810, and my night shots often have a strong moire when I export them from Lightroom at 640x640 (optimized for Instagram).   This photo was shot at f2.8, ISO 4000, 15 seconds with a Nikkor 17-35mm. Does anyone know why this is happening?? $P[X=x]=0$ when $X$ is continuous variable I know that for continuous variable $P[X=x]=0$.   But i can't visualize that if $P[X=x]=0$, there is infinite number of possible $x$'s. And also why do their probabilities get infinitely small ? Why can I not place a pregnant woman to work but others work while pregnant? I am playing Fallout Shelter, have 3 kids in my shelter, all going well, thought I would make one more kid with big strength numbers and decent agility/perception (kids take on SPECIAL stats from their parents). All the women who are pregnant work in my shelter, apart from this one. She can not me put to work, can not be moved from the living shelter, can not be moved to a job via the clipboard short cut.  TL;DR One of the NPC females who is pregnant can not be put to work, can not be moved from the living shelter room, she just walks about as if she is carrying a mammoth inside her. I have NOT moved the shelter, have not let the dad die, have not done anything at all.