Conditional Multivariate Normal (beyond the bivariate case)
Conditional distributions of the multivariate normal
Base-b Representation of an Integer: Why can I make the assumption about number of terms in expansions in uniqueness part?   Reading the book of Koshy I have come across the below theorem. It states that I can write any integer $N$ in a base $b\ge2$ representation $N=a_kb^k+...+a_1b+a_0$ such that $0\le a_i&lt;b$, $a_k \neq 0$ for some $k\ge0$.  In the uniqueness part, why can I assume the expansions contains the same number of terms ? I must prove that all expansions of $N$ equal the one in the theorem, but if I add terms to the expansion by zero coefficients, well, then the expansion is not in the proper form anymore ? (the greatest term in the expansion is $0$ if I add zero coefficients) .  Can someone help clear this out ?     Why can I assume the expansions contain the same number of terms ? If I add terms to the expansion, well then I've violated the form of the expansion ? I accidentally changed /var owner/group to my username and then changed it back to root, but not all the /var folders' owners are root, so is there anyway to change back owner/group of files/folders to default state?  Or at least those files/folders that are created by packages? How to export debug logs? I spend my days waiting on the Force.com Console and it makes me crazy, I have a pretty nice machine and it still chokes on the details sometimes.  Anyways, I saw  had given a  and is presenting again this year Dreamforce '12.  However, it seems like they're presentation is targeted at using their product, or for that matter others like it (, ) on Heroku, and not really targeting APEX/VisualForce development!  Is this the case? Are there any better solutions out there for reviewing logs?  Are there any APIs that allow you to export your debug logs out of SFDC programatically? Or has anyone even tried to tackle this? Why is "the set of all sets" a paradox, in Layman's terms? I've heard of some other paradoxes involving sets (i.e., &quot;the set of all sets that do not contain themselves&quot;) and I understand how paradoxes arise from them.  But this one I do not understand. Why is &quot;the set of all sets&quot; a paradox?  It seems like it would be fine, to me.  There is nothing paradoxical about a set containing itself. Is it something that arises from the &quot;rules of sets&quot; that are involved in more rigorous set theory? I have notice some sites have the same form for login, register and forgotten password.  Below the form you have 3 buttons    i forgot my password register log me in   What are the pros and cons on using this approach and which version would you go for. Where were the Avengers during Iron Man 3? I don't want my users to change the system wallpaper. How do I the lock the wallpaper down? Update  Users are changing wallpaper by right clicking the picture and choosing set as wallpaper. How to restrict this behaviour?  Is it possible to remove Backgrounds Tab from Appearance Preferences? If yes how? I run a guest ubuntu 12.04 on a host ubuntu 12.04, with VirtualBox, and the guest is much, much slower than the host (ALT+TAB takes 4-5 secs). I had a look around and I found contradicting opinions on VirtualBox versus VMware (free); so I thought to keep the former.   Both systems are updated, I installed the additions on the guest and I evenly split memory and video memory (64MB) between guest and host. I am running a Toshiba m200 laptop with 4GB ram and shared video memory. The host bios does not include a configuration option for machine virtualization. I have 2 cpus and I can't give them both to the virtual machine.  Is there anything I overlooked that could solve my problem?  Feel free to ask for more info, and thank you for any help.  EDIT Idling with the system monitor open the (single) guest cpu never gets below 55% and could rise to 80 - 90% just by moving the mouse around. Opening Firefox will cause the system monitor to show cpu usage 100% in the guest, while the host shows that both cpus are evenly working around 60%.  My cpu is Intel® Core™2 Duo CPU T5450 @ 1.66GHz × 2.  If this is not a configuration problem, does it mean my machine is too weak for virtualization? Agreement in "[Singular Noun] Is/Are [Plural Noun]"? My fish's native habitat is rice fields. My fish's native habitat are rice fields.   Which one is correct? I'm pretty sure it's the first, since 'is' modifies 'habitat,' but it still sounds weird... I want to install Win Xp on my Ideapad Z 570 laptop but i always get blue screen with message with some drive related problem which asks me to run CHKDSK command. I tried with that but no luck. Is there any way i can install Win Xp with SP 2 ?  Edit: i searched across the sites and came to know there could be some Compatibility problems, and i could fix it by setting HDD mode to IDE; will it solve the problem? How do you teleport a certain player to spawn after they win a 1v1 I managed a KitPvP server in Minecraft and everything works fine except when players wants to duel each other. They get sent to a room where they will be dueling. The main problem is when the winner wins, I have no idea how to teleport them back to spawn. The names of the derived functors $\operatorname{Tor}$ and $\operatorname{Ext}$ seem quite cryptic to me. Does anyone know what these abbreviations stand for? I would be glad if someone could tell me where these names come from. Display sheet name in Google Spreadsheets Is there any way to display a sheet name as the result of a function in a Google Spreadsheets (exactly like , except in Google Sheets)? SqlServer: can one table's PK be the FK of two table's? I have three tables project, users and proj_user. The PK of proj_user table is the FK of project and users table's pk e.g.(project_id,user_id)  My question is, is it possible if the project_id and user_id's data is different  like project_id = '12345' and user_id = 'abc987'  Please reply  kind regards Vivek How to re-index the values of an array in PHP? Possible Duplicate:          I installed the IE10 beta on Windows 7. It has an annoying autocorrect feature like the one in MS Word that messes up everything I write. How do I disable it? Bernoulli numbers, taylor series expansion of tan x I found the following formula here: .  Taylor series of $\tan x$:  $$\tan x = \sum_{n\,=\,1}^\infty \frac {(-1)^{n-1}2^{2n} (2^{2n}-1) B_{2n}} {(2n)!} x^{2n - 1} $$.  I do not understand what the Bernoulli number means in this formula. My problems are the following ones:  I do not know anything about Bernoulli numbers. I do not know how to expand the Bernoulli number in the formula you see further up. What expansion will be the final result? How did you arrive there? Why did you arrive there? How did you know that you should use the specific Bernoulli-related terms that you used in your answer? What is the purpose of the Bernoulli number in this formula?  A great deal of thanks. How to convert a std::string to const char* or char*? I need to exclude .git from my find search. To achive that, I am using the -path ./.git -prune switch:  $ find . -path ./.git -prune -o \( -type f -o -type l -o -type d \) | grep '.git' ./.git   However, even though this skips the contents of the .git directory, it lists the directory itself. It works when I add -path ./.git -prune -o -print -a  find . -path ./.git -prune -o -print -a \( -type f -o -type l -o -type d \) | grep '.git'   Why is this necessary. I thought that both commands should have same output. The second syntax is quite ugly. Why don't I need to install any Drivers for Ubuntu