I am quite embarrassed to ask you this question but I am stuck.  I have to compute the following conditional expectation : $E[\theta|x_i,y]$. I know how to compute the basic E[X|Y]E[X|Y] but I definitely do not know how to compute E[X|Y,Z]E[X|Y,Z]. Can someone please orient for the first step?  with   $\theta\sim N(0,\sigma_\theta^2)$  $y=\theta+\eta$, where $\eta\sim N(0,\sigma_\eta^2)$  $x_i=\theta+\epsilon_i$, where $\epsilon_i \sim N(0,\sigma_\epsilon^2)$  I know the result is $$E[\theta|x_i,y]=\frac{\sigma_\eta^2}{\sigma_\epsilon^2+\sigma_\eta^2}(x_t-y)+y$$ but I cannot find it.  I know how to compute the basic $E[X|Y]$ but I definitely do not know how to compute $E[X|Y,Z]$. Can someone please orient for the first step?   Thank you
Suppose $X,Y$ and $Z$ are multivariate normal with means and full covariance matrix. The conditional expectation $E(X | Y)$ is well know. What is the conditional expectation of $E(X | Y,Z)$ if $Y$ and $Z$ (and $X$) are correlated? Standard textbooks only seem to cover the case when $Y$ and $Z$ are uncorrelated.
I installed Ubuntu (twice actually) onto the same drive. I wanted to 'try again' since one of them didn't install correctly and the other installed differently, but it worked.   I was getting frustrated with the GRUB menu because it was really sloppy (There were two Windows options - one with the Windows bootloader to go into Ubuntu, and two different versions of Ubuntu from the first install for some reason and memtest, etc.).  In my attempts at getting rid Ubuntu to do a fresh installation, I went ahead and deleted the partitions that weren't swap or main via Windows 7. As I said, I am a noob.  Now, even though I though I completely got rid of Ubuntu, including the GRUB menu, when I boot my PC I am brought directly to GRUB Rescue. And from what I've found from other forums, GRUB rescue isn't even completely functional for me (it doesn't recognize any commands that it should support besides ls. It also returns unknown filesystem for any partition I try to view or boot.)  Is there any way that I can boot straight into Windows? I fear I may have gone about deleting those partitions in the wrong way. If so, what are my options? Simple way to see a list of installed iOS apps with their storage space size? Countable set of truth assignments satisfying set of well formed formulas I am trying to answer the following question posed in my logic class: (throughout we work in propositional logic) is there a set $S$ of well-formed-formulas (wffs) satisfied by countable set $V$ of truth assignments such that any truth assignment satisfying $S$ lies in $V$?    My guess is no.  My first reaction to this was to do a diagonalization.  Present $V$ as an array with $v_{i, j}$ the truth value that assignment $v_i$ gives to the $j$-th propositional letter.  Obviously the hard case is when $S$ is infinite; if $S$ is finite, then only finitely many propositional letters occur in the $S$-formulae.  Then there is some maximal $k$ for which all $A_n$ with $n \geq k$ do not occur in V.  Then the diagonalization is trivial: just diagonalize from the $k$-th letter onward, since changing $A_k$ in this range doesn't affect anything in $S$.  But I have little clue about how to approach the main case when $S$ is infinite. I thought maybe I should try using the fact that $S$ is consistent (since it's satisfiable).  If it's maximally consistent, then I think this is simple too, since for every propositional letter $A_n$, either $A_n$ is in $S$ or $(\neg A_n)$ is in $S$, implying that there is only one truth assignment satisfying $S$--since every truth assignment must agree on each propositional letter.    But if $S$ is not maximally consistent, this isn't available to me.  Somehow I would like to show that infinitely many propositional letters do not occur in $S$.  Then I can apply the trick above and just diagonalize through the superfluous letters.    So, yes, just looking for some hints or corrections if you have any please, though maybe if I don't get anywhere on my own I'll give up and ask for more.  Thanks.  (By the way, by referring to letters that "occur in $S$" I mean letters that occur in some formula in $S$). I'm training a neural network for regression. The input vector consists of $140$ entries.   For each feature vector entry, I calculate both min and max over the training set. The difference max-min of some entries are smaller than 1e-5. I understand I can normalize such feature entries by say MinMaxScalar. However, if the difference max-min is this small, can I discard such entries since they seem to be so insensitive? I'm giving training to a large group of people remotely and will be covering a number of application shortcut keys.  I've seen 's on-screen display of keystrokes; is there a similar product for Windows?    The other features of MousePose (fancy mouse pointers, etc.) aren't really useful to me, just the OSD of key presses. Can you fake a closed question? [‌closed] I just had a random thought; what if you append "[closed]" to the end of a question title. Is it filtered out, or in some way disallowed?  If you are seeing this, it isn't. It could potentially be used for some trickery, right? Or maybe not. I don't know, that's why you're here: discuss!  EDIT: Just a recap: Juan Manuel edited and removed "[closed]" from the end of the title and then answered (see below) - but it is technically possible.  Edit 2: Looks like it's still possible, if you play silly tricks with Unicode. (There's a  character in the new title.) What if I accidentally run command "chmod -R" on system directories (/, /etc, ...) I accidently ran  sudo chmod 755 -R /   instead of  sudo chmod 755 -R ./   I stopped it after few seconds, but now there is some problems such as  sudo: must be setuid root   How can I revert permissions back? "This edit would have to be a suggested edit" / edit button grayed out A couple of times recently when I attempted to edit a post while reviewing it from the "First Posts" queue, I received the following message when I tried to submit the form:  This edit would have to be a suggested edit. (x)   This is a rather cryptic message, considering that edits made from a review are suggested edits, subject to the same peer review process. There was no indication of how the edit would have to be submitted differently, much less why. I searched both help and meta for more information about this message, but came up empty.  The first time it happened, after I cancelled out I saw that someone else had just edited the post, so I thought maybe that's why I couldn't submit an edit from the review (and wondered why, if that's the case, the error message didn't just say that instead of telling me something that doesn't make any sense - that the edit I'm trying to suggest can't be submitted because it would have to be a suggested edit). However, the second time I received this message (last night, for this question: ), there was no other edit. So, I clicked the No action needed button and tried to edit the post outside the review process, only to discover that the edit link was grayed out.   I see several explanations of possible causes for graying out the edit link here: . However, there was no tooltip when I hovered over the disabled link, and the edit queue was in the single digits.  A few minutes later, I noticed that the edit link was no longer grayed out, so I edited the post and my edit was accepted.   My best hypothesis based on my experience with the error so far and the explanations I've read here at meta is that someone submitted a suggested edit while I was reviewing the post, which (a) caused me to get the cryptic error message and (b) caused the edit link to be grayed out when I accessed the post the normal way. Then a few minutes later, the suggested edit was rejected, opening up the question for new edit suggestions.  Rather than speculating about it and trying to determine the answer scientifically, it would be helpful if someone could give me the answer (as Seinfeld fans might put it, "Why don't you just tell me why I can't edit the post?"). It would be even more helpful if the error message itself provided the explanation, or if the message were defined somewhere in the help pages. But, at the very least, hopefully there will soon be an answer on meta to enlighten people who scratch their chins over this in the future. :) 'had better not entangle' v 'had better not to entangle' Can I write this sentence:     He said Carter had better not entangle the US in problems like those   in Afghanistan, Somalia and Iraq.   Like this:     He said Carter had better to not entangle the US in problems like those   in Afghanistan, Somalia and Iraq.   ?  If so, what's the difference between the meaning of both sentence? I want to prove or disprove this problem: If there exist $\lim\limits_{x\rightarrow \infty} (f'(x)+f(x))=L&lt;\infty$ then $\lim\limits_{x\rightarrow\infty} f(x) =L$.  When I assume problem below:  If there exist $\lim\limits_{x\rightarrow\infty} (f'(x)+f(x)) =L&lt;\infty$, There exists $\lim\limits_{x\rightarrow\infty} f(x)$?  I can use mean-value theorem to show that.  So my question is:     If $\lim\limits_{x\rightarrow\infty} (f'(x)+f(x))=L&lt;\infty$, does $\lim\limits_{x\rightarrow\infty} f(x)$ exist? Class not found loading JDBC org.postgresql.Driver Is it possible to get the data off of the hard drive of a PlayStation 3 that has crashed? I have already voided the warranty so I am not worried about that and I have access to quite a few tools.   I have a new PlayStation and a few saves that were not backed up. I am not worried about them but if it is possible I would love to get it moved over.   The old PlayStation will not turn on at all and I think I am going to have to pull the drive. My main concern is if I am able to transfer the files without running into any issues. I have heard that some of the stuff is specific to each PlayStation, is that true? Minecraft looks like a bad texture pack I am playing Minecraft 1.12 but today the in-game textures look much lower quality than usual. I don't have any of the super secret settings turned on, and I'm unsure how to fix this and get the normal textures back. How to reach local computer via machine name instead of IP? Developer here prototyping a mobile app, somewhat new to mobile:   I have a simple HTTP service running (currently) on my main laptop with machine name latitude. Another laptop named vaio sharing the same WiFi network can access that service via http://latitude:8080 -- in other words, it can easily resolve the (current) IP 192.168.x.y (or whatever dynamic IP it has at that moment) of latitude somehow. Now my HTC Android phones, connected to the same WiFi network, can reach the IP address of latitude so opening in its browser http://192.168.x.y:8080 works. But I'd like to use the machine name here, too, like when I access the HTTP service from vaio, simply by typing http://latitude:8080 and have the phone resolve the current dynamic IP of latitude. This doesn't work, only get the standard browser error page: "Webpage not available".   Is there some DNS setting in Android I need to tweak? Haven't found anything from playing around with Settings, and a question like this is notoriously hard to google, too...  The One V has Android 4.0, and the One M7 has Android 4.2 in case that makes a difference.  (Note, this should work even when the Android is not USB-connected to my computers and is not acting as a WiFi Hotspot -- obviously, since it's consuming my main WiFi network anyway). Is it correct to say "I kindly request you to..."? Isn't kindness already implied when you say "I request you to..."?  When I say "I humbly request you to...", the word humbly helps me to label the state of my behavior during the request.  On the other hand, what value does the word kindly add to the request? Wifi hotspot software package other than ap-hotspot? I am trying to show the current date in my JSP page using JSTL. below is the code I am using.  &lt;jsp:useBean id="now" class="java.util.Date" scope="request" /&gt; &lt;fmt:formatDate value="${now}" pattern="MM.dd.yyyy" /&gt;   But the above code is not producing any results? Am I missing anything here or is there any better approach for this? I am using JSTL 1.1. What lubricants can be safely added to a laptop fan? I've got a fan in a laptop that occasionally makes some loud airplane-like noises.  It mostly happens about 10 seconds after booting up and lasts for 10-20 seconds.  It also occasionally happens when the computer is running, but very rarely.  Interestingly, it does not seem to happen when the processor is being used heavily.  The laptop does not have a discrete graphics card.  The fan is clean.  I'm not sure if the laptop is under warranty, but I trust my own skills much more than I trust the manufacturer (or the shipper).  Before I search for a matching fan and replace it, I thought I would see if it is safe to try any lubricants.  Are there any lubricants that are safe to use inside a laptop?  I don't want a fire or anything that will splatter and cause conductivity issues within the circuitry. How do I protect random people pointing their domain to my server? What exactly is a kilogram-meter? This question isn't just about kilogram-meters, it's about multiplied units in general.  I have a good mental conception of divided units, e.g. meters per second or grams per cubic meter.  Meters per second just (usually) means how many meters are traversed by an object each second.  Simple.  But I don't really have a mental conception of what it means when units are multiplied, e.g. a kilogram-meter.  Can anyone explain in simple physical terms what a kilogram-meter is?