If I flag a comment from a mod, can the same mod review my flag? If I flag a comment from a mod, can the same mod review my flag?
Should moderators be allowed to decline flags on their own comments? I think I just witnessed a moderator decline a flag raised on his own comment. (I'm hesitant to discuss specifics unless I have to, as I don't mean to put anyone in a negative light.)  Since there are at least 2 other moderators per site, I'm not sure this should be allowed—I feel that either   only uninvolved moderator(s) should be able to view and handle flags on co-moderators' posts, or moderators should be able to view all flags, but a flagged moderator should not be allowed to decline a flag against him- or herself.   I have no personal issue with this moderator. I just felt in this case that there was truth in both sides (the moderator's as well as the flagging user's), and sought a win-win solution, i.e. by improving the disputed answer. Coming back an hour later to see that the moderator unilaterally declined the user's flag—that didn't seem fair to the user...  I am making some assumptions based on the "Last Seen" stat in the moderator tools, so if I'm simply mistaken on what happened, I apologize in advance.
Does $G\cong G/H$ imply that $H$ is trivial? Assume the standard situation, that is, let $X_1, \ldots , X_n$ be independent and identically distributed with $X_k ∼ P_\theta(x; \theta)$ , where $P_\theta(x; \theta) = 2x/\theta^2$  if $0\le x \le\theta$ and $0$ otherwise. It is required to estimate $\theta$. Show that the maximum likelihood estimator for $\theta$ is $\hat{\theta} = \max{[X_1, \ldots , X_n]}$ and then show that the cumulative distribution function of $\hat{\theta}$ is $F_\theta(z) = z^{2n}/\theta^{2n}$. Here's what i did so far: Maximum Likehood estimator: $L_x(θ) = \prod_{i = 1}^{n} P_θ(x_k)$ Here we have $P_θ(x_1,...,x_n;θ) = P_θ(x_1,θ).P_θ(x_2,θ)...P_θ(x_n,θ)$ Likehood = $L_{x,θ}(θ) =P_θ(x_1,θ).P_θ(x_2,θ)...P_θ(x_n,θ)= 2x_1/θ^2. 2x_2/θ^2.. 2x_n/θ^2 = [2^n.\prod_{i = 1}^{n}x_i]/θ^{2n}$ Log-likehood: $\sum_{i = 1}^{n}log(P_θ(x_1,...x_n;θ))= \sum_{i = 1}^{n}log(2x_i/θ^2)$ Is this correct so far? Im still not sure how to get to $\hat{θ} = max{[X_1, . . . , X_n]}$ As for the the cumulative distribution part to show $F_θ(z) = z^{2n}/θ^{2n}$: $F(z) = P(max({x_k})&lt;z) = P(x_1&lt;z).P(x_2&lt;z)..P(x_n&lt;z) = 2x_1/θ^2.2x_2/θ^2...2x_n/θ^n = 2^n.\prod_{i = 1}^{n}x_i/θ^2n$ Not sure if this is correct. Would really appreciate some help. Edit: From the answers below, we can deduce the the estimator is biased. What estimator would be unbiased? How can i find it? Function $f(z)$ is holomorphic at least within the unit disk.   If for all arguments $|z|&lt;1$ we have $|f(z)| \le 1$, and there exists a zero of order $n$ at $z=z_0$, then show that $|f(0)| \le |z_0|^n$.  How should I tackle this problem? Can it be generalized if for $|z|&lt;R$ we have $|f(z)| \le M$ ?    So far I only understand that there exists a holomorphic $g(z)$ with $g(z_0) \ne 0$ such that $f(z) = (z-z_0)^n g(z)$,then $|f(z)| = |z-z_0|^n |g(z)| \le 1$ and moreover $|f(0)| = |z_0|^n |g(0)|$, but that doesn't seem useful since apparently I know too little about $g(z)$. In particular why should $|g(0)| \le 1$? What's the deal with a leading underscore in PHP class methods? While looking over various PHP libraries I've noticed that a lot of people choose to prefix some class methods with a single underscore, such as  public function _foo()   ...instead of...  public function foo()   I realize that ultimately this comes down to personal preference, but I was wondering if anyone had some insight into where this habit comes from.  My thought is that it's probably being carried over from PHP 4, before class methods could be marked as protected or private, as a way of implying "do not call this method from outside the class".  However, it also occurred to me that maybe it originates somewhere (a language) I'm not familiar with or that there may be good reasoning behind it that I would benefit from knowing.  Any thoughts, insights and/or opinions would be appreciated. Apex PMD: Problem: Validate CRUD permission before SOQL/DML operation Background   I am using the Apex PMD plugin for VS Code and it's giving me this problem:     Validate CRUD permission before SOQL/DML operation   For this line of code:  insert contentVersion;   Which is part of this method:  private void attachReport(Id recordId) {      ContentVersion contentVersion = new ContentVersion(         versionData = Blob.valueOf(buffer.toStr()),         title = 'Import Report',         pathOnClient =  StringUtils.format('/Import-Report-{0}.txt', DateTime.now().getTime()),         FirstPublishLocationId = recordId);      insert contentVersion; }   Questions    Why am I getting the problem? What should I do to not get the problem?     Reference Switching OS remotely using TeamViewer I have a dual boot system with Ubuntu 16.04 and Windows 7. Windows 7 is automatically booted (default in the bootloader). On both OS I have TeamViewer installed.  When I'm working remotely and want to switch to Ubuntu I have to reboot the PC but then automatically Windows is booted again (I'm not in front of the PC, so I cannot use the bootloader). How can I in such a case switch to Ubuntu, i.e. starting Ubuntu? And how can I switch back to Windows? In many C/C++ macros I'm seeing the code of the macro wrapped in what seems like a meaningless do while loop.  Here are examples.  #define FOO(X) do { f(X); g(X); } while (0) #define FOO(X) if (1) { f(X); g(X); } else   I can't see what the do while is doing.  Why not just write this without it?  #define FOO(X) f(X); g(X) Graduate student in or of? In my cover letter I want to write that I am a graduate student in statistics. But I am not sure about the "in". So what is correct?     I am a graduate student in statistics.      I am a graduate student of statistics. In formal logic, how is it possible for an argument with a contradictory conclusion to be valid? I've recently been trying to introduce myself to formal logic, and I've hit a stumbling point:  In the text I'm reading, a valid argument is defined as "an argument in which it is impossible for the premises to be true and at the same time the conclusion false."  The text then later prompts me to declare whether it's possible for an argument to be valid with a contradiction for a conclusion. The answer key then claims that yes, it is in fact possible, but offers no further explanation. I'm also supposed to create an example.  I just can't wrap my head around this one.  Here's the example I've worked up, is this a valid argument?   If grass is green then it is raining.  If water is wet then it is not raining.  Therefore: It is raining and not raining.   My head hurts. How to render world position pass A world position pass is a pass used for composting other elements into the scene after the initial render. In a world position pass the R, G, B values correspond to the X, Y, Z axis (or X, Z, Y). A world position pass could look something like this. (Image form another 3d app)    Is there a way to render out corresponding world space coordinates of each pixel? Prove inequality using Jensen's inequality I'm trying to find the birth certificate of my wife's great grandmother who was probably born in Durban, South Africa in 1884. I'm currently unable to find any online resources for this.  If such a thing does not exist online, is there any other method of retrieving a copy or at least just the details? Determining the name of the VMware host of a VM guest - from the guest Could someone please explain the role of the transistor in this circuit? I have a feeling it has to do with the LC circuit but I'm not sure and don't understand completely. The following is an image of the circuit (the transistor is n-type. It is used in lots of sensors to detect and generate ultrasonic waves. Can hypercomputation compute the impossible? There are things which are illogical/logically impossible (like saying that 2+2=4 and 2+2=5. Without changing anything in the axioms of mathematics or logic, this would be a contradiction and would be inconsistent and illogical/logically impossible.   There are other types of logic systems apart from classical logic, like paraconsistent logics or even trivialism, that allow these contradictions to occur, prove them as right and work with them.   We can make a paraconsistent or trivialist system and work with it. For example, with trivialism, in theory, we would be able to derive and state everything we would want (since literally everything, even including illogical/logically impossible inconsistencies and contradictions), but we as humans (or as brains), are limited and can't conceive everything we want (at least to what I know). Therefore, no matter how many trivialist models we create and how much time we would work with them, we would never find or conceive many illogical/logically things because they are just that: impossible. There are impossible things to describe and conceive. For example, Russel's set is the set of all sets that do not contain themselves. If Russel's set contains itself, then it cannot contain itself, since it only contains sets that don't contain themselves. But if Russel's set does not contain itself, then it must contain itself, since it contains all sets that don't contain themselves.  There are quite a few logic bombs like this. You cannot ever compute the contents of Russel's set, and there are more formal, mathematical ways to present it. All of them have in common that you can't actually compute what the set is, whether you do it by hand, in your head, or on a computer. It's just a statement that cannot be fully logically processed.  If you take every possible state the human brain can be in, none of them include the computation of Russel's Set's contents. That is, not only can the contents not be computed, they cannot even be represented. No stimulus can cause us to comprehend Russel's Set, since such comprehension is not possible to begin with. It does not have a solution. Even if we try to solve it using trivialism, we would just be able to write a solution that does not make sense and prove it has sense and it is the real solution, but we could not be able to have a solution that would make sense "outside" the realm of trivialism (for example in classical logic), even though, using trivialism, we could prove that such solution would have sense in whatever context and logic system.   But what about hypercomputational machines (for example oracle-like machines)? I've read about some models of hypercomputation which are compatible with paraconsistent or trivialism logics. I've also read there are some models of hypercomputation (particularly those oracle-like models which use a black box) where, essentially, the hypercomputer is an algorithm that cannot exist. It might be because such an algorithm is fundamentally forbidden by logic itself (which is hided in a black box). Would any of these be capable of computing/"conceiving" these impossible things I wrote before? Do you know of anything that would help? I have seen some examples about using "in" with time expressions. They give some examples as shown below:     I will leave for vacation in a month. (Exactly one month from now I   will go on vacation.)      We’ll be there in an hour.  (Exactly one hour will go by and then we   will arrive.)   But these comments confused me. Then I looked the usage of "in" up in a dictionary and it says about usage of "in" with time expressions :"before or at the end of a particular period". I think the comments and the definition in the dictionary contradict each other?    I have examples of mine:     1- Dinner will be ready in ten minutes. (Maybe dinner will be   ready at the 5th minute? or 8th. Does it strictly mean dinner will be   ready at the end of the ten minutes?)      2- My letter arrived in two days. ( Does that mean it took   exactly two days to arrive? or Could it be just one day because he/she   doesnt remember the exact time?)      3- Imagine you are on the first day of a month and your friend says:   I will be going outside the country in this month. (Does that mean he/she could go tomorrow or ten days later or at the end of the   month?)      4- He can run a mile in 5 minutes. ( Does that mean he has to   spent entire 5 minutes to run a mile? Could it be 4 or 4.5 minutes?) Why does the zoom sometimes stop at a point? I often find that I can zoom in to a point, but then cannot zoom any more, even when there is a lot of room to zoom to the meshes on the scene.   This is particularly annoying in the following scenario:  I often land up left clicking on the scene and the 3D cursor shifts there. I use Shift+C to shift the 3D cursor back to the origin. However, this also centers the view on the cursor and shifts the view to show all objects, and sometimes this zooms things way out &ndash; at this point, if I try to zoom in, I can zoom in to a point (using the pinch/zoom on trackpad), but then it stops zooming in.   How do I zoom in after that? Is there anything else I am doing wrong in this case? For the Fibonacci numbers, show for all $n$: $F_1^2+F_2^2+\dots+F_n^2=F_nF_{n+1}$ Is there a way to access Windows file with administrative rights using WSL?  sudo vi /mnt/c/Users/a/admin/file.txt Is there a way to disable the hotkeys? I navigate with Ctrl-n,p,f,b (readline/ keys), so that I don't have to move my hands too much and get  again. Is there a way to disable Ctrl-b being hotkey for bold?  Note that this is not just an Emacs thing. Standard web browsers, like Firefox and Chrome, use things like  Ctrl + K and Ctrl + L to navigate to the Google search bar and address bar respectively.