[answered elsewhere - duplicate]
Note: I am posting a question from a former student of mine unable to post on his own for technical reasons.  Given an iid sample $x_1,\ldots,x_n$ from a Weibull distribution with pdf $$ f_k(x) = k x^{k-1} e^{-x^k} \quad x&gt;0 $$ is there a useful missing variable representation  $$f_k(x) = \int_\mathcal{Z} g_k(x,z)\,\text{d}z$$and hence an associated EM (expectation-maximisation) algorithm that could be used to find the MLE of $k$, instead of using straightforward numerical optimisation?
How do I align an image to centre? How do I align an image to centre?  In a beamer presentation I have a 2-3 items on a slide followed by an image. The image is not wide enough to cover whole slide, so it leaves around 30% space from right. How do I adjust it to leave enough space on both sides?  \begin{frame} \frametitle{Outlook} \begin{itemize} \item apps \item apps \item apps \includegraphics[scale=0.3]{P2P}     \end{itemize} \end{frame} I am a Chinese citizen holding a HK SAR passport. How long am I able to visit the UK within a 365-day period?  My stamp is for 6 months. Could I leave within 6 months but re-enter again a couple of weeks for another 6 months? Say for a game with irregular hotspots (say Risk, or a strategy game like Paradox's Hearts of Iron or Crusader Kings), how do you   Define a non-rectangular hotspot of irregular shape (much like a territory on a map?), in code? What tool can you use to trace out the hotspot and import into your game? What is the algorithm for detecting if someone has clicked within such a hotspot? If $A^2 = I$, then $\operatorname{rank} (A+I) + \operatorname{rank} (A-I) =n$ If $A^2 = I$ where $A$ is an $n\times n$ matrix, then why is $\operatorname{rank} (A+I) + \operatorname{rank} (A-I) =n$.   I am not sure why this seems to be true. What is the relationship between size of object with distance? How does the size/length of an object vary with distance?   Is it a logarithmic relationship? exponential? linear?   I plotted a curve of the size/length of an object for different distances from the camera, and the curve looked exponential/logarithmic. I was trying to understand the reasoning behind that. Dark Energy / Accelerating universe: naive question In electromagnetism, why does nature prefer the right-hand rule over the left-hand rule? On-screen keyboard popping up whenever I touch screen I'm in 17.10. Whenever I touch the screen, whether to change windows/apps, scroll within a browser, or press a button, the stupid little keyboard pops up in the bottom left corner.  I have never left Screen Keyboard enabled in Universal Access, but if I toggle it on, that's the same keyboard popping up in the bottom left corner.    In this screenshot, I'm simply touching the screen in a full-screen youtube video. You can see the menu pop up on the right, under the point where I'm touching.  I don't have a before pic, but it was similar look/color keyboard, but it was smaller, maybe half as wide, and only in the bottom left section of the screen, as opposed to stretching across the entire width. This change from little left-hand keyboard to full-width keyboard happened after following @pomsky 's advice below.    This is a . You can mark yourself affected by it to hopefully increase its received attention. The use of nominative "whom" (as in “persons whom it is foreseeable are likely to...”) I'm from Western Pennsylvania. Until I moved away, I never realized that when I omitted the to be from phrases like needs to be cleaned, my usage was different than what most English speakers are accustomed to. Is it wrong? Concurrently interleaving execution of Lua and TeX in LuaTeX The usual way to interleave Lua and TeX in generating documents is by invoking Lua from Tex through the \directlua facility and generate Tex from Lua using tex.print().  For example, consider the Plain LuaTeX:  \directlua{     es=""; someluatex = function () tex.everypar="PAR!" end     tex.print("one", es, "two")     someluatex()     tex.print("three", es, "four") } five\bye   Looking at the document LuaTeX generates for that input, we see that someluatex() is run before the Tex backend does anything with the output: the PAR!s will be inserted before "one" and "two", as well as after "three".  Is there best practice for ensuring that TeX code issued by some Lua code is issued before some other LuaTeX code?  There are several ways to do this: with some code I am working with I am trying the following scheme:   Wrap the code executed by the \directlua in a coroutine, call it myco; At the point we want to ensure the Tex so far tex.print-ed is executed, use:  tex.print("\\directlua{coroutine.resume(myco)}") coroutine.yield()  If everything is in order, the Lua will resume after the Tex is processed.   This is not ideal, however: we must ensure that the TeX backend is in the right state to understand the \directlua command, which may not always be the case.  Is there a better way to achieve this? Is there a standard and accepted method for selecting the number of layers, and the number of nodes in each layer, in a feed-forward neural network? I'm interested in automated ways of building neural networks. How to prove the inequality $2\sqrt{n + 1} − 2 \le 1 +\frac 1 {\sqrt 2}+\frac 1 {\sqrt 3}+ \dots +\frac 1 {\sqrt n} \le 2\sqrt n − 1$? Prove that for any positive integer $n$, $$2\sqrt{n + 1} − 2 \le 1 +\frac 1 {\sqrt 2}+\frac 1 {\sqrt 3}+ \dots +\frac 1 {\sqrt n} \le 2\sqrt n − 1$$ Progress I think Riemann sum should be used for the middle term. I got the limit as $n\to \infty$ of the function inside using Riemann sum but what I cannot get are the lower and upper bound. Lightning Components Basics: Attributes and Expressions Trail The error :      The Packed field is either not using the lightning input component,   the checked value of the item's Packed__c attribute or the correct   type of input.   My Code:  &lt;aura:component &gt;     &lt;aura:attribute name="item" type="Camping_Item__c"                      required="true"                     default="{Name:'Tent', Price__c:100, Quantity__c:1, Packed__c:true}"                     /&gt;         &lt;p&gt; The Item is &lt;ui:outputText value ="{!v.item}"&gt;&lt;/ui:outputText&gt;&lt;/p&gt;          &lt;ui:outputText value="{!v.item.Name}"/&gt;     &lt;lightning:input type="toggle" label="Packed" name="togglevalue" value="{!v.item.Packed__c}" /&gt;     &lt;lightning:formattedNumber value="{!v.item.Price__c}" style="currency" currencyCode="USD" currencyDisplayAs="symbol"/&gt;      &lt;lightning:formattedNumber  value="{!v.item.Quantity__c}"/&gt; &lt;/aura:component&gt; Migrating from Evolution to Thunderbird How to fix error W: Target Packages (main/binary-amd64/Packages) is configured multiple times in my sources.list file? How do I reference the only element in a singleton set? You can turn any element $n$ into a singleton set by adding braces, $\{n\}$. Is there an inverse to this operation, such that if I know the set is a singleton set I can easily reference its element?  For example, say I have the set $A = \{5,6,7,8\}$, and then some process that iteratively eliminates all but one element of $A$, and then I want to see what 10 plus the resulting element is, how could I write that?  The only way I can think of is by referencing the first element by its index, e.g., $10 + A_1$. Is there another way to do it though? In my case the elements of $A$ are already indices, so I would have to index an index, like $10 + x_{A_1}$. Which is not the worst thing in the world, I was just wondering if there is a better way. The message that appears in the reputation tab of a user's profile when they gain or lose reputation due votes disappearing when another user is deleted is simply:     user was removed   This message is confusing and unhelpful. Below are comments that demonstrate this confusion, . I don't have any quotes from the users who could not find it and remained confused.  There is , and . However, the message has not been changed.  I know that in the past the developers have been reluctant to direct users to meta in some situations, such as question bans, because it may cause users to post here appropriately. That does not seem to apply to this case. This is not typically a case of ""; most of us have probably seen the message at some point.  Why is this message vague and unlinked? What negative behaviour does this confusion mitigate?       My first interpretation was that I was the user who was removed!        I just simply wished the explanation on the reputation page was better. Seems like I shouldn't have had to come to the meta section to figure this out.        It must be better to show "User  was removed". For a moment I just thought that I was removed :-(        the information should be better. I lost 10 points yesterday by "user removed" and assumed that I was the one being removed, leaving me wondering why and feeling somewhat embarrassed.         The recalc policy is fine. But the red mark and "user was removed" looks cryptic and unnecessarily negative--especially since the only user name mentioned on a profile is one's own. So the natural impulse is to bind "user" to the account you're looking at. (It was jarring to me and I could tell what it meant, but still this could be clearer.) I agree that orange is better than red and ideally all of these things would have hyperlinks to a help page (or at least a meta post) explaining what the deal is.        +1 (to HostileFork) for the idea of linking to an explanation of 'User was removed'. It just took me 10+ minutes to find this particular thread and read through, when I could have simply clicked through! I would also like a little more info on why user was removed (abuse, friend upvotes, rules, etc) , as that could help educate the community as a whole on what behaviors to report.        I could care less about the rep gain or loss, but when you have a loss it is a scary message without context. I honestly thought for a moment that my account had been inhibited in some way. No, it didn't say "Your account was removed." Still, there is that moment of "what did I do wrong?" which seems silly to cause simply by not posting a few extra words. A clearer "A user who voted on your posts was removed along with reputation changes they caused" would have gone a long way to not cause me to question my participation in the review queues as of late.         My problem is that the message "user has been removed" is not a clickable link like the other messages - so I had to search meta to discover this question to find out what it meant. Can we clarify to the OP that their question is not yet closed and the duplicates are only suggestions? I have recently installed ubuntu 11.10. But when i try to install a software it tries to 'updating cache' but after a while, it stops, showing:                            Failed to download repository information                           Check your internet connection   so, now i am totally unable to install any software in my ubuntu.  Please,let me know how to solve the problem.