Replacing background image using jQuery not working
Switching a DIV background image with jQuery
Convergence in Distribution in Order Statistics Let $X_1, X_2, \ldots$ be iid from Exp$(\theta)$ with density function $f(x) = \frac{1}{\theta}e^{-\frac{x}{\theta}}$. (a) Find the limiting distribution of $M_n = Y_1 - \theta\ln(n)$ and $T_n = nY_n$, where $Y_1$ and $Y_n$ represent the first and last order statistics (among $n$ observations) respectively. Answer: I have obtained the CDF of X to be: $$F_x(x) = 1 - e^{-\frac{x}{\theta}}$$ the CDF of $Y_1$ to be: $$F_{Y_1} = 1 = e^{-\frac{xn}{\theta}}$$ the CDF of $M_n$ to be: $$F_{M_n}(x) = \left[1 - \frac{1}{n}e^{-\frac{x}{\theta}}\right]^n$$ with limiting distribution $$e^{-e^{-\frac{x}{\theta}}}$$ the CDF of $T_n$ to be: $$F_{T_n}(x) = 1 - e^{-\frac{x}{\theta}}$$ which is also the limiting distribution. (b) Show that $M_n$ and $T_n$ are asymptotically independent. Answer: I've tried finding the joint PDF for ordered statistics by using the equation $$g_{ij}(y_i, y_j) = \frac{n!}{(i - 1)!(j - i - 1)!(n - j)!}[F(y_i)]^{i - 1}[F(y_j) - F(y_i)]^{j - i - 1}[1 - F(y_j)]^{n - j}f(y_i)f(y_j)$$ however, it is a mess based on my CDFs. Any suggestions on a different approach? Bmp to jpg/png in C# How to vote on friends / colleagues ' questions (or answers) Almost every time a colleague of mine asks a question, we have discussed this problem beforehand. Also, we sometimes meta-discuss the question for stackoverflow (why did I get the &quot;this might be subjective&quot; warning, is this understandable enough, etc). This is less so with answers, but I could believe for some groups this works the same. For now I'll stick to questions, but you could s/question/answer if you like. The resulting question is almost always  Interesting for me, and a problem I don't know the answer to. I probably would favorite it According to me a valid and good question (as we talked about it beforehand) I would probably want to upvote it.  Now I believe to read that &quot;ring voting&quot; is a thing, and I tried to find some questions about this, but didn't find many. I did find and read this blogpost from 2008:  . It reads to me that upvoting 'fraud' is more commonplace then downvoting and it might seem anomalous that I would upvote almost all questions from one user. If all colleagues would do this to their team, you'd get some mediocre questions getting a lot of votes, and some users getting a lot of attention, points etc from that. If you would -as seems to be done -, sort the amount of upvotes for my colleague, you'd get me being 'anomalous' in front of the crowd. On the other hand, as explained above, I do want to upvote almost all stuff some of my colleagues put on here for (I believe) the right reasons: they are questions I consider good and interesting. It's just that I know of all their questions (as they tell me about them), which obviously isn't the case for a random user. So what is the deal?  When is upvoting content from one user frowned upon? Would my usecase be in danger of being a (what I consider 'false') positive for the fraud-detection? (and would you agree with that or not) How to prevent this false positive (if you agree with me it is one, otherwise this is a moot question) -&gt; As noted in the comments: I'm not looking for tricks, so an answer could be &quot;don't vote for your colleagues&quot;. I agree that there should be no to 'tricks' around that could be used for real fraud of course Does it look good to edit the question you're answering? I have a question about editing practices:  Does it look good to edit a question you have just answered?  For example: say I had just answered a question, then saw that the question had some minor formatting issues. Should I edit it? Does it turn up voters off when they see that I am answering a question I changed, possibly to better suit my answer? What is the Big-O of a nested loop, where number of iterations in the inner loop is determined by the current iteration of the outer loop? What is the Big-O time complexity of the following nested loops: for (int i = 0; i &lt; N; i++) {     for (int j = i + 1; j &lt; N; j++) {         System.out.println(&quot;i = &quot; + i + &quot; j = &quot; + j);     } }  Would it be O(N^2) still? How to text-to-speech output using command-line? How to get speech output from entered text by using command-line?  Also facility to change speech rate, pitch, volume etc using simple command. Trying to format USB (using Linux/fdisk) so it shows up on my Mac I have a USB drive that I can see/access/modify/etc in Linux/Ubuntu but it doesn't show up on my Mac OSX.  I did sudo fdisk /dev/sdb (where my USB is) and then g to create a new GPT partition table, n to make a new partition, used all default settings, then w to save and exit.  Then I did sudo mkfs.fat -F32 /dev/sdb1 to format the partition with a FAT32 filesystem.  I ejected the USB and put it in my Mac and it doesn't show up / get detected.  What did I miss? How to list all functions in a Python module? Finding derivative of $\sqrt[3]{x}$ using only limits I need to finding derivative of $\sqrt[3]{x}$ using only limits  So following tip from : I multiplied top and bottom by conjugate of numerator  $$\lim_{h \to 0} \frac{\sqrt[3]{(x+h)} - \sqrt[3]{x}}{h} \cdot \frac{\sqrt[3]{(x+h)^2} + \sqrt[3]{x^2}}{\sqrt[3]{(x+h)^2} + \sqrt[3]{x^2}}$$  $$= \lim_{h \to 0} \frac{x+h-x}{h(\sqrt[3]{(x+h)^2} + \sqrt[3]{x^2})}$$  $$= \lim_{h \to 0} \frac{1}{\sqrt[3]{(x+h)^2} + \sqrt[3]{x^2}}$$  $$= \frac{1}{\sqrt[3]{x^2} + \sqrt[3]{x^2}}$$  $$= \frac{1}{2 \sqrt[3]{x^2}}$$  But I think it should be $\frac{1}{3 \sqrt[3]{x^2}}$ (3 instead of 2 in denominator?)  UPDATE  I found that I am using the wrong conjugate in step 1. But this (wrong) conjugate gives the same result when I multiply the numerator by it. So whats wrong with it? (I know its wrong, but why?) What is the difference between an abstract method and a virtual method? What is the difference between an abstract method and a virtual method? In which cases is it recommended to use abstract or virtual methods? Which one is the best approach? Newman's "Natural proof"(Analytic) of Prime Number Theorem (1980) I am trying to understand this short proof by newmann. I faced some problems while grasping this very proof. Please help me out.  1 . I am not clear, why in step (1)'s proof he says that from unique factorization and the absolute convergence of zeta we have... [here factorization makes sense but where did he use absolute convergence to prove (1).]  2 . Step 2 is clear but where will he use it (may be I will out later as i am still working on next steps.  3 . My major problem is to understand step 3rd's last part that i put it in the red box. please elaborate it. I didn't understand anything in this box.  I am still working on the next steps of the proofs. If i get any problem in them i will ask you.  Thank you so much in advance. SQL Server 2012 and 2016 Standard:  If I put if-else logic in a stored procedure to execute one of two branches of code, depending on the value of a parameter, does the engine cache the latest version?  And if on the following execution, the value of the parameter changes, will it re-compile and re-cache the stored procedure, since a different branch of the code must be executed? (This query is quite expensive to compile.) Can we set privacy for "last seen" status? This is a very simple question but I believe it's nontrivial.  I would like to know if the following is true:      If $R$ and $S$ are rings and $R[x]$ and $S[x]$ are isomorphic as rings, then $R$ and $S$ are isomorphic.    Thanks!  If there isn't a proof (or disproof) of the general result, I would be interested to know if there are particular cases when this claim is true. What insect is this? (India) Can anyone tell me what kind of insect (if it is one) is this...!! Or is it the pupa of some insect?  Well I don't think that the whole big thing is the insect itself, it appears to be just a kind of protection or shelter which moves along with the tiny little thing that keeps on popping out and going it so as to move. Location:  India Default behavior of "git push" without a branch specified Determinant of circulant matrix Find the determinant of the following matrix in the terms of $a_1,a_2,\cdots,a_n$ explicitly, $$ \begin{bmatrix} a_1 &amp; a_2 &amp; a_3 &amp; \cdots &amp; a_n\\ a_2 &amp; a_3 &amp; a_4 &amp; \cdots &amp; a_1\\ a_3 &amp; a_4 &amp; a_5 &amp; \cdots &amp; a_2\\ \vdots &amp; \vdots &amp; \vdots &amp; \ddots &amp; \vdots\\ a_n &amp; a_1 &amp; a_2 &amp; \cdots &amp; a_{n-1}\\ \end{bmatrix} $$ When the determinant is zero? I want to run Notepad++ twice. Like in this paint printscreen.  How I want it:    Not what I want:    Is this possible? Adding a Link to a Field in a Field Set? String queryFields = null;              for(Schema.FieldSetMember field : SObjectType.Task.FieldSets.Activity_Detail_Page.getFields()){                  queryFields = (queryFields == null ? field.getFieldPath() : queryFields+', '+field.getFieldPath());               }                String query = 'Select '+queryFields+' from Task where Id=\''+activityId+'\'';               task = Database.query(query);   i'll creating a field-set,now how do i add link on any field?  above code is  for dynamically query creation . below code of page   &lt;apex:pageBlock title="Activity" id="Block1"&gt;       &lt;apex:pageBlockSection title="Activity Detail"&gt;         &lt;apex:repeat value="{!$ObjectType.Task.FieldSets.Activity_Detail_Page}" var="field"&gt;             &lt;apex:outputField value="{!Task[field.fieldPath]}" /&gt;         &lt;/apex:repeat&gt;     &lt;/apex:pageBlockSection&gt; &lt;/apex:pageBlock&gt;    As per the image attached, I want to add a link in Rounded field that liks to account. Can any one help me? I have recently noticed a rather large amount of small worms in the fresh cod I am buying. I have tried to take them out as much as I can and of course have spoken to my fish supplier about them, but he assures me they are harmless. However, I don't believe my customers would be as assured. Is it okay to serve this fish, taking into account I might miss a worm or two?