If  $X \sim N(0,{a^2})$,  $Y \sim N(0,{b^2})$ and   $Corr(X,Y) = \rho $,   then can we say that $(X,Y) \sim BVN(0,0,{a^2},{b^2};\rho )$?  If this is true, then can someone please tell me how can I proceed to show this mathematically?  Thanks!
Somebody asked me this question in a job interview and I replied that their joint distribution is always Gaussian. I thought that I can always write a bivariate Gaussian with their means and variance and covariances. I am wondering if there can be a case for which the joint probability of two Gaussians is not Gaussian?
Hide trivial comments Recursive grep vs find / -type f -exec grep {} \; Which is more efficient/faster? Why not to extend the set of natural numbers to make it closed under division by zero? We add negative numbers and zero to natural sequence to make it closed under subtraction, the same thing happens with division (rational numbers) and root of -1 (complex numbers).  Why this trick isn't performed with division by zero? How to avoid pressing Enter with getchar() for reading a single character only? Light fixture with a switch that has an outlet I hope this explains it better: in this room there is a switch with one set of wires and only the black one went through the hole in it, and another black one in the other hole, and is hooked to the outlet by being wrapped around the screw terminals. The ground is cut short and not grounded.  Now on to the outlet: the wire from the switch is connected to the top screw - but it's on the side that says "white".   There are two more sets of wires that connect to the outlet as follows:   the two black ones are on the the other screw terminal on the bottom (one on the "white" side)  the grounds are grounded to the screw terminal below that  the white ones are connected by the one from the switch to the bottom (black side), with one of the white ones from the other set on the screw terminal, and the one from the other cable is on the top screw terminal on the "white" side.   Now to the light: there are the black and white that come out of the box, and that is the set that has the ground cut short.  The original light fixture was a single 660w/250v rated socket.  The one my friend put up was a fixture with two 660w /250v sockets.  At the light only black and white connected, not ground... It worked then made noise and this is where I'm at.  When I wire test them, the black one from the switch and the white ones from either sets nothing...  but all the other ones light up.....! How should I approach obvious proofs like these    I have been trying but couldn't find an elegant way to work these. Any help is highly appreciated ! Especially looking for a nice proof/hint for first problem Size of VARBINARY field in SQL Server 2005 I am trying to determine the size in bytes of the contents in a VARBINARY(MAX) field in SQL Server 2005, using SQL. As I doubt there is native support for this, could it be done using CLR integration? Any ideas would be greatly appreciated. I wanted to take a sneak peek at Windows 7 so I thought of installing it. I have Windows Vista on my laptop which came pre-installed with it. I didn't want to mess with it.  So I created a partition (20 GB) in my USB external hard disk and tried to install Windows 7 on that partition. But when I booted from a Windows 7 DVD and selected the target partition on USB hard disk, it said it cannot be installed.  Is there any way to install Windows on an external USB hard disk? Why is $\mathbb{R}^2$ not a subspace of $\mathbb{R}^3$? Add an image directly from the clipboard I've tried to find other questions covering this, but (surprisingly) I did not find any.  When I want to add a screenshot to a post, as far I know the only way to do it is to save it as a file and then upload the file, using Stack Overflow's image hosting. OK, much better than finding a hosting site yourself, but sometimes I wish I could just paste the image from the clipboard.  It's not as straightforward as it may seem, I know. , and it needs a Java applet to get it done. What does standard deviation tell us in non-normal distribution In a normal distribution, the  imparts standard deviation a lot of meaning, but what would standard deviation mean in a non-normal distribution (multimodal or skewed)? Would all data values still fall within 3 standard deviations? Do we have rules like the 68-95-99.7 one for non-normal distributions? Which meta am I supposed to post on? I'm mostly active on  and we have a separate . Most of my questions on IT Security meta have answers with links here. So my question is, where am I supposed to post what i.e. feature request, bug report, behavior questions? Capistrano for Django Finding a clear difference between truth and fact I have been starting back in school after a long hiatus.  In one of my classes, a discussion of Truth began.  The problem I have had is that no one seems to have a solid definition between the two.   My earlier training and schooling left me with this definition, and I would like some feedback.  Fact - A point of data that can be directly qualified/quantified through confirmed, standardized measurement.  Truth - A point of data not directly qualified/quantified through confirmed, standardized measurement.  So fact would be that ice cream is cold, as we can place a measurement of the temperature.  Ice cream being tasty would be truth, as it is impossible to accurately measure "tasty".  Please let me know your thoughts. Tsunami dampening mechanisms Encouraged by the zeitgeist let me ask the following:  Is it feasible (now or in the future) to build systems a certain distance of a vulnerable coastline which can serve to dampen a tsunami before it reaches the coast itself?  The following picture comes to mind. We have some device which is small enough to be mounted on a buoy. An array of such buoys can be anchored some distance off the coastline, controlled by computers which are linked into the global tsunami warning network. This setup is quite feasible given what a cell phone can do today.  On the detection of an oceanic earthquake or other tsunami generating event (such as a piece of the Rock of Gibraltar falling into the sea) and given present environmental conditions one can calculate the expected path of the tsunami and its intensity. If a TDS (Tsunami Dampening System) of the type I describe above happens to be deployed in range of the tsunami, all relevant information is conveyed to the TDS controllers by the global tsunami warning system. All this happen in a matter of moments.  This leaves plenty of time (25min - 2hr) for the devices in the TDS array to be activated and to do their job. The question in this case would be - what form could such devices take? Perhaps mini-turbines which could dissipate the incoming energy into the ocean by first converting it to electrical energy.  Any such undertaking involves physical estimates for the size and shape of such an array, the precise capabilities of each device, etc. Many of these concerns involve simple physical questions.  Can you come up with the details of such a system or alternatively outline your own design? If you think that this idea would never work in the first place - for technological, physical or some other reasons - please explain what you think would be the prime obstacle and why? Using Illustrator CS6 to create shape out of multiple paths Where can I find my .emacs file for Emacs running on Windows? I tried looking for the .emacs file for my Windows installation for Emacs, but I could not find it. Does it have the same filename under Windows as in Unix?  Do I have to create it myself? If so, under what specific directory does it go? Solving a cubic polynomial equation. Overview I have tried finding a solution to this problem myself and I have flailed. Its just a challenge for me. could you please tell me how far am I in solving this question? My approach for quadratic equation : I am still a student, and when I first saw the quadratic formula I wanted to derive it myself and I did it. This was my logic: the equation $x^2 + bx + c=0$ is obviously supposed to contain 2 roots (real or imaginary). So any 2 points in an axes can be represented as: $n+k$ or $n-k$. so (1) : putting $x = n+k$, (2): putting $x=n-k$ we get two equations; on subtracting $(1) - (2)$ we get an equation in $n$ and $k$ as, $4nk+2kb=0$ which gives $n=-b/2$.  Now substituting this value of $n$ in $(1)$ and $(2)$ and adding them we get $k= (+or-) \sqrt{b^2 -4c}/2 $. My approaches for trying to solve cubic equations: Let $x^3+bx^2+cx+d = 0$ be the equation. My first trials were focused on extracting the roots by various substations. Let me explain some of them. Originally, when I derived the quadratic equation, I wanted to literary &quot;represent the solution&quot; by $n+k$ and $n-k$. most methods that I have thought of for cubic equation similar to that of the quadratic (like assigning 3 unambiguous  variables to uniquely represent 3 roots- $n$ and $k$ represents unique values), by considering 3 unique values, but they end up being ambiguous. Then I was suddenly struck with the idea that I could define certain random operators to &quot;transform&quot; the equation in some way changing the co-coefficients of $x^2, x, x^0$. I have defined the first transformation as: $x^3+bx^2+cx+d=0 \to x^3+ b'x^2 + c'x+d' =0   $ then $b' = b$, $c' =b^2+c$, $d' = bc-d$. Applying this operation changes the modified equation's zeros as follows: $\alpha'=(\alpha+\beta)/2, \beta' = (\beta+\gamma)/2, \gamma' = (\alpha+\gamma)/2 $ if the initial zeros are $\alpha, \beta, \gamma$. My latest assumption is that creating $n$ number of transformations and applying them can help us obtain the roots in some combination. The other operation I have defined is &quot;increment roots by by $\theta$ operation&quot;. in this case, $x^3+ bx^2+ cx+ d \to x^3+b'x^2+ c'x+d=0$. here, $b' = b + 3\theta, c' = 3\theta^2+ 2\theta b+ c, d' = \theta^3 +b\theta^2 + c\theta + d$. This modification transforms the original roots $\alpha, \beta, \gamma$ to $\alpha' = \alpha + \theta, \beta' = \beta + \theta, \gamma' = \gamma + \theta$ Now for my questions: How far am I from solving the cubic polynomial problem myself without any external help? More over, I give up. How to find the roots of a cubic equation? Could my latest idea for solving cubic equations actually be applied (the transformation method)? Is it possible to find the roots with my transformation method? (my second transformation definition was successful in converting the coefficient b or c to zero by transforming the roots linearly) Showing that $\mathbb{R}$ and $\mathbb{R}\backslash\mathbb{Q}$ are equinumerous using Cantor-Bernstein I need to prove that $\mathbb{R}\backslash\mathbb{Q} \sim \mathbb{R} $  Using Cantor-Bernstein, need to show an injection from $\mathbb{R}\backslash\mathbb{Q}$ to $\mathbb{R}$ and from $\mathbb{R}$ to $\mathbb{R}\backslash\mathbb{Q}$.    $\mathbb{R}\backslash\mathbb{Q}$ is a subset of $\mathbb{R}$ so only need to show injection from $\mathbb{R}$ to $\mathbb{R}\backslash\mathbb{Q}$ to complete the proof.    Possible injection: $f:\mathbb{R}\to \mathbb{R}\backslash\mathbb{Q}$ defined as $f(x) = \pi x$ if $x$ is not a multiple of $\pi$; otherwise $f(x) = \sqrt{2} x$.    Not sure if $f$ actually is an injection... Is $x^x=y$ solvable for $x$? Given that   $x^x = y$; and  given some value for $y$   is there a way to expressly solve that equation for $x$?