If $X = N_x$ and $Y = 4*X + N_y$, where $N_x$, $N_y \sim N(0, 1)$, then we have that $P(Y|X=x) = N(4x, 1)$. If we want to then find $P(X|Y=y)$, I would think that Bayes would work:  $P(X|Y=y) = P(Y|X=x)P(x)/P(y) = N(4x, 1)P(x)/P(y)$.   For x=2, the solution is N(8/17, 1/17). I don't see how this results. Can someone clarify please?  EDIT: Another user cited this as being a duplicate, but I don't see why.   EDIT: Originally, I asked "what is $P(x)$, $P(y)$? Are they the pdf of $N(0, 1)$ at their respective values?"
How do I complete the square from the point I have left off at, and is this correct so far?   I have a normal prior for $\beta$ of the form $p(\beta|\sigma^2)\sim \mathcal{N}(0,\sigma^2V)$, to get:  $p(\beta|\sigma^2)=(2\pi\sigma^2V)^\frac{p}{2}\exp[-\frac{1}{2\sigma^2}\beta^T\beta]$  where $\beta^T\beta$ is   $\sum\limits_{i=1}^p \beta_i^2$.  My likelihood has a normal distribtuion for the data points y of the form $p(y|\beta,\sigma^2)\sim\mathcal{N}(B\beta,\sigma^2I)  $  $p(y|\beta,\sigma^2)=(2\pi \sigma^2V)^\frac{n}{2}\exp[-\frac{1}{2\sigma^2}({\bf y}-{\bf B}{\bf \beta})^T({\bf y}-{\bf B}{\bf \beta})]$  (Note that $\beta$ is a matrix/vector too, \bf does not work.)  To get my posterior for $\beta$ I combined the above, took the exponential parts only, and then expanded to get:  $\exp[-\frac{1}{2\sigma^2}({\bf y}^T{\bf y}-{\bf y}^T{\bf B}\beta-\beta{\bf B}^T{\bf y}-\beta^T{\bf B}^T{\bf B}\beta)]\exp[-\frac{1}{2\sigma^2}({\bf \beta}^T{\bf B})]$.  I dropped the $({\bf y}^T{\bf y})$ term, as is not a function of $\beta$.  Putting into one expression without the exponential:  $-\frac{1}{2\sigma^2}(-{\bf y}^T{\bf B}\beta-\beta{\bf B}^T{\bf y}-\beta^T{\bf B}^T{\bf B}\beta+{\bf \beta}^T{\bf B})$.  I know I need to combine the similar terms and get into the form of the multivariate normal distribution, which is what I am aiming for, but I am unsure how to do this? I probably have to add an extra term to the expression to get it into the correct form?  Note: This is not homework, it's a project, but my Bayesian working knowledge is not good at all and so I need to understand the working out. I intend to integrate out the $\beta$ and then the $\sigma^2$ after getting into the multivariate form.
Take most recent (or concatenate) edit comments when editing during grace period I want to find an example of a homomorphism $f:G\to H$ such that $A$ is a normal subgroup of $G,$ but $f(A)$ is not so in $H.$  I know that if $f$ was onto $f(A )$ must be normal , but otherwise i want to find an example! How to create a cross-browser sub document with iframe or shadow dom? made me think about the movie versions of the 7th book.  In Deathly Hallows Part II      Voldemort has Nagini attack Snape because Voldy thinks that Snape has the Elder Wand's allegiance. We know that Snape didn't actually have the allegiance, Draco did (and by then Harry did) and his plan had failed.   But if Voldy's plan had succeeded with Snape, would he have gotten allegiance?      Since voldemort didn't kill Snape, Nagini did... Short circuit or disconnect to bypass a compressor I have an Altec Lansing ATP3 2.1 audio system PCB which I reverse-engineered, and I would like to bypass the JFET compressor that's on it. Its active components are a JFET and four op-amps. I will connect the input to the output so it gets forwarded to the next stage.  My question is: should I disconnect the input and output from the compressor (in that case should I remove power supply as well, which would be very annoying), or can I leave it connected but short-circuited?  The block I want to short-circuit is the pink one on the left.    I realize the image is very small. The sound comes in on the right, in the green box. In the middle yellow box there's some trebble/volume/bass control. The small green box on its left merges the left and right channels to forward it to the subwoofer section, which is the complete left half of this diagram (except the red box on the left, which is just power). Signal then goes through a low-pass, a small equalizer and a compressor (the big purple box). It finally gets amplified in the brown power amp. How Does One Transfer A Steam Game? I have a failure to transfer my game from one HDD to another, and one PC to another. I copied the entire Skyrim folder from one HDD to another. And told where to find it also. Steam did a huge check of my HDD.  But it ended up downloading most of the files anyway. It took a week to download Dawnguard, Hearthfire, and Dragonborn files along with my Hi-Res textures.  I did ask about it in chat. But I feel this could help me or somebody else.  This is the screen I am looking at after transferring my entire hard drive to to new one. Steam downloaded my games, including Skyrim even though my Skyrim data folder had all the data files for Dawnguard, Hearthfire, Hi-Res and Dragonborn.  I have my copied files and have got rid of everything not steam related. I just have my DLCs and they include my hires files.  This is what it looks like.    But I still get this :     What could be causing this? How can I rectify? And in future when one is migrating to a new PC, how can this be avoided?  EDIT::::::::::::::::: Removed everything : Here is how it looks :  Still the prompt as before Steam Error 15  (Side Note : I transferred all my Origin games just by copy/pasting. This really is not nice.)    EDIT 2 :::::::::::::::::::::  And one more EDIT  I tried getting game cache up to speed, but this is prompt I am getting. But I played the game, it was working, I could pick out my character and all, and escape from Helgen.  EDITED 3 :::::::::::::::::  How does one transfer a Steam game? A game that is heavily modded, will the backup a Steam Game option suffice? Can I leave the UK and come back in, on a Tourist visa? Incorrect indentation for tag listing questions loaded via AJAX I am seeing a weird indentation for questions loaded via AJAX (i.e., by clicking the n question(s) with new activity link). 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This is my small set of code to get its output:  Process p = Runtime.getRuntime().exec("C:\\j2sdk1.4.0\bin\\helloworld.java"); BufferedReader input =         new BufferedReader(new InputStreamReader(p.getInputStream())); while ((line = input.readLine()) != null)    System.out.println(line);  input.close();   This was my set of code but this throws an IOException. I have a Python script that will need to be given to a client.   We are currently evaluating what license level the client will need in order to run the script for their software acquisition purposes.   We all have ArcGIS 10.1 Advanced license in our company.   I checked all the tools and extensions used in the script against the web help and found that they should work on the Standard license level.   Is there a way I can test the script against the Standard license level, when we have no Standard license level in or company (only the higher Advanced level)?