Variance of a predicted $y$ when $x_0$ is given?
Linear regression prediction interval
When reading lens reviews on the Internet, I often find subjective statements about the image quality that a lens produces, such as "good contrast" or "sharp". The problem is that I don't think I am capable to actually see these qualities on an image. I don't even think I could tell the difference between a cheap kit lens and a top lens, if not by "this just looks better".  So my question is: without looking at sharpness tests and MTF curves, how do you learn to judge the quality of a lens based only on sample images? What are the characteristics you look for and what constitutes good or bad in each of them? What happens if you do sudo passwd without specifying a user? I wanted to change my own password (as an admin) so I did the following command:  sudo passwd   and then it prompted for a password but when I tryed to relog, my password was not changed. I'm now wondering what password did I changed since it did prompted me to enter a password but I'm not sure what password did it changed exactly.  I know that if I do sudo passwd &lt;MY_USER&gt; it works, I'm just wondering without a user what happens.  Thank you Closing Reject Suggested Edit dialogue freezes review process If you go to review a suggested edit and close the Reject dialogue box, the button at the top-right will continue to say "Rejecting...". You will not be able to continue with the review process.  I have refreshed the page, and tried clearing my cache. If I refresh the page, I can continue reviewing the edit.  I'm using Chrome Version 31.0.1650.57 m. When proving $\bar x$ and $S^2$ are independent in my noted it says that "functions of independent quantities are independent ". Can someone tell me how functions of independent quantities are independent happen?  Also let $X_1,X_2,X_3,\dots,X_n$ be a random sample.And suppose we want to estimate parameter $\theta$ using $T(x)$ as an estimator. In this I have a expression as $E\{ [  T(X)-E(T(X))][E(T(x)-\theta)]\}$.  I want to know if I can say that in $[T(X)-E(T(X))]$ since $E(T(X)$ (expected value is a one particular fixed value) and $T(X)$ are independent of one another. Also the expression $[E(T(x)-\theta)]$ is independent of $X$.  Hence the two expressions $[T(X)-E(T(X))]$ and $[E(T(x)-\theta)]$  are independent of one another. So that I can use if $a,b$ are independent $E(ab)=E(a)E(b)$ form How can I downgrade a package to an older version via apt-get?  Other tools are also acceptable but apt-get is preferred. I have a simple query:  select * from countries   with the following results:  country_name ------------ Albania Andorra Antigua .....   I would like to return the results in one row, so like this:  Albania, Andorra, Antigua, ...   Of course, I can write a PL/SQL function to do the job (I already did in Oracle 10g), but is there a nicer, preferably non-Oracle-specific solution (or may be a built-in function) for this task?  I would generally use it to avoid multiple rows in a sub-query, so if a person has more then one citizenship, I do not want her/him to be a duplicate in the list.  My question is based on the similar question on .  UPDATE: My function looks like this:  CREATE OR REPLACE FUNCTION APPEND_FIELD (sqlstr in varchar2, sep in varchar2 ) return varchar2 is ret varchar2(4000) := ''; TYPE cur_typ IS REF CURSOR; rec cur_typ; field varchar2(4000); begin      OPEN rec FOR sqlstr;      LOOP          FETCH rec INTO field;          EXIT WHEN rec%NOTFOUND;          ret := ret || field || sep;      END LOOP;      if length(ret) = 0 then           RETURN '';      else           RETURN substr(ret,1,length(ret)-length(sep));      end if; end; Monochromatic squares in a colored plane I've been making a map for 1.10 and it's going great, but 1.11 shows great mobs to use for it. However, most things have channged in command syntax. For example, /kill @e[type=ArmorStand,r=6] is now /kill @e[type=Armor_Stand,r=6]  What about /testfor? I can't find a way to testfor a player to stand on a block and give them an effect.   What's is going on in this image is that a redstone clock is running into this command /testfor @a[1117,20,507,r=1] (if I was to stand on them cords the comparator would turn on and power that command block), but it only works in 1.10... from 1.11 snapshots, I've seen some errors of it, like it now needs to have {} at the beginning and end of it. (e.g. /testfor @a{[1117,20,507,r=1]})   It's still not working, though, so does anyone know how to get it to work? Thanks to the internet, graphic design and programming are becoming increasingly overlapping fields.   As a programmer, I constantly find myself needing basic knowledge of Graphic Design, but have trouble locating thorough yet concise graphic design learning resources, and instead usually find bits and pieces of knowledge applicable to the task at hand.  Can you guys offer some tips or recommend some good books, tutorials, blogs, and websites which provide a beginner level overview of web design that have been, in your experience, effective and high quality learning materials. I'm not looking for tips on how to use image editing tools, but assuming a basic grasp of those, which resources and advice will best help a new designer create professional looking designs? Click to hide in the Hero content is not aligned correctly for the non joined communities The "Click to hide" icon in the hero content (welcoming message) for the non joined communities are not aligned correctly for most of the private beta and some other communities.  A few examples are:        Can the icon be aligned to the right hand side with correct padding? Let me start this with : Very long "About me" text squeezes both the left side (flair) and the right side (the section with location, GitHub link, etc.)  Now, the reverse thing has happened:         put a long text in their "location", and it causes the right section to be overly extended, effectively squeezing the About Me section.  When will the squeezing game end? I have recently started using blender and one of the models I'm working on has dark shadows along edges. I started this model from scratch. I can't remember them being there when I first started the model, but I had trouble joining areas together and think I've pressed something I shouldn't have. However, there are so many options I'm not sure what I did.  Here is an image of what I mean   The one on the left has the shadow. As a test I started a new model, which is on the right in the image, and as you can see it doesn't have any shadows.  Also, occluded vertices partially show through the model. Occlusion doesn't work properly.   In orthogonal view small darkened triangles appear along the the edges.    I don't really want to start the model again from scratch so any ideas on how to remove this shadow would be great. Thanks. Handling circular entity references with Migrate I am using  on a Drupal 6 to Drupal 7 migration right now.  I have three types: type1, type2, type3.  Each of the three types has a entityreference field on it, which is configured to be able to point to all three types.  This means that there can be circular references, and when a particular node is being migrated, the destination node may not exist yet and could potentially be any of the three types.  My migration class looks like this:  class MyNodeMigration extends DrupalNode6Migration {   public function __construct(array $arguments) {     parent::__construct($arguments);      $this-&gt;addFieldMapping('field_legacy_nid', 'nid');      $this-&gt;addFieldMapping('field_the_reference', 'field_the_reference')       -&gt;sourceMigration(array('type1', 'type2', 'type3');   } }  $node_arguments = array(   array(     'class_name' =&gt; 'MyNodeMigration',     'description' =&gt; 'type1',     'machine_name' =&gt; 'type1',     'source_type' =&gt; 'type1',     'destination_type' =&gt; 'type1',     'dependencies' =&gt; array('roles', 'users'),   ),    array(     'class_name' =&gt; 'MyNodeMigration',     'description' =&gt; 'type2',     'machine_name' =&gt; 'type2',     'source_type' =&gt; 'type2',     'destination_type' =&gt; 'type2',     'dependencies' =&gt; array('roles', 'users'),   ),    array(     'class_name' =&gt; 'MyNodeMigration',     'description' =&gt; 'type3',     'machine_name' =&gt; 'type3',     'source_type' =&gt; 'type3',     'destination_type' =&gt; 'type3',     'dependencies' =&gt; array('roles', 'users'),   ), );  $common_node_arguments = $common_arguments + array(   'user_migration' =&gt; 'users', );  foreach ($node_arguments as $arguments) {   $arguments = array_merge_recursive($arguments, $common_node_arguments);    Migration::registerMigration($arguments['class_name'], $arguments['machine_name'], $arguments); }   When I run the migrations, most nodes are fine, but I get a decent amount of Stubs (*) created.  Some of the destination nodes have the entityreference pointing to these Stub nodes.  The source nodes are fine.  What I have uncovered is that the bundle on the destination nodes that are being made as stubs are incorrect, and look like they are all type1.  A node of the proper type does end up being created, but it never gets set as the entityreference target.  Another way to explain this is that I end up with   node: nid=123, type=type1 node: nid=234, type=type1, field_the_reference=123 node: nid=345, type=type2   where it should be   node: nid=234, type=type1, field_the_reference=345 node: nid=345, type=type2   How do I handle this situation?  (*): a "Stub" in the context of this question here refers to a node which is created for the purpose of being a reference target, but does not get its data initially. The term is used throughout the Migrate documentation and source code. How to link dataframes in ArcGIS or QGIS? The below image shows a layout in ArcGIS 10.1 with four dataframes.  Each dataframe is of the same geographic area, although they are different images. For example, the top left image is a 1989 DOQ, the top right image is a reversed 1989 DOQ, the bottom left image is a 2012 DOQ, and the bottom right image is a reversed 2012 DOQ.   Is it possible to link the dataframes so that panning the image in one dataframe pans the images in all of the other dataframes (i.e. similar to how you can "Link Views" in Erdas Imagine)? Is this possible in QGIS? How does the Rectified Linear Unit (ReLU) activation function produce non-linear interaction of its inputs? When used as an activation function in deep neural networks The ReLU function outperforms other non-linear functions like tanh or sigmoid . In my understanding the whole purpose of an activation function is to let the weighted inputs to a neuron interact non-linearly. For example, when using $sin(z)$ as the activation, the output of a two input neuron would be:  $$ sin(w_0+w_1*x_1+w_2*x_2) $$   which would approximate the function  $$  (w_0+w_1*x_1+w_2*x_2) - {(w_0+w_1*x_1+w_2*x_2)^3 \over 6} + {(w_0+w_1*x_1+w_2*x_2)^5 \over 120} $$  and contain all kinds of combinations of different powers of the features  $x_1$ and $x_2$.   Although the ReLU is also technically a non-linear function, I don't see how it can produce non-linear terms like the $sin(), tanh()$ and other activations do.  Edit: Although my question is similar to , I'd like to know how even a cascade of ReLUs are able to approximate such non-linear terms. Can you please check my Cesaro means proof I wanted to prove the following:  if $x_n \to x$ then $y_n \to x$ where $$ y_n = {x_1 + \dots + x_n \over n}$$  Please can you tell me if my proof is correct? My proof is this:  Let $\varepsilon &gt; 0$. Fix $N$ such that $n &gt; N$ implies $|x_n - x| &lt; {\varepsilon \over 2}$.   Then $\left |{1 \over n} \sum_{k=N+1}^{N + n} x_k - x \right | &lt; {\varepsilon \over 2}$. Now let $M$ be such that ${|x_1 + \dots + x_N | \over M} &lt; {\varepsilon \over 2}$ and $M &gt; N$. Then  $$ \left | \sum_{k=1}^M {x_k \over M} - x   \right | \le  \left | \sum_{k=1}^N {x_k \over M}   \right | +  \left | \sum_{k=N+1}^M {x_k \over |M-N|}  - x   \right | &lt; \varepsilon $$ Here the proof is finished. But one can observe:  It is possible that $y_n$ converges even if $x_n$ doesn't: If $x_{2n} = 0$ and $x_{2n + 1} = 1$ then $x_n$ does not converge but $y_n \to {1 \over 2}$. Unbiased estimator of a uniform distribution How prove that $\lim\limits_{x\to+\infty}f(x)=\lim\limits_{x\to+\infty}f'(x)=0$ if $\lim\limits_{x\to+\infty}([f'(x)]^2+f^3(x))=0$? Question:     Let $f$ be differentiable on $[0,+\infty)$, such as$$\lim_{x\to+\infty}\left([f'(x)]^2+f^3(x)\right)=0$$show that $$\lim_{x\to\infty}f(x)=\lim_{x\to\infty}f'(x)=0$$   I think this problem is similar to  and (the  background)  For my problem I guess that if  $$\lim_{x\to+\infty}\left([f'(x)]^{2m}+f^{2n+1}(x)\right)=0,m,n\in N^{+},n,m&gt;1$$ then we have $\lim_{x\to\infty}f(x)=\lim_{x\to\infty}f'(x)=0$. arithmetic progression of primes Prove that there is no arithmetic progression that consists only of primes.  A question that I've been set; I'm guessing it makes use of primes being written in the form 4k+1 and 4k+3? Not sure where to start.  Thanks. In the series finale, Admiral Janeway travels back to 2378 to take Voyager back to Earth. Out-of-universe, of course, this point in time was chosen to fit in with the continuity of the rest of the series. In-universe, however, it seems that Janeway could have chosen any point in time, since she had the ability to travel to and from the Delta Quadrant at will. Is there a reason given, in-universe, for why she chose that particular incident to travel back to?