I noticed that there is a definition of the p-value in my textbook. It is defined as the p-value of a composite null hypothesis and it says the following:    I have no idea why it is written with a supremum. I've spent hours pondering this, does anyone have enough of a background to help me with this? Thank you!
I noticed that there is a definition of the pvalue in my textbook is defined says the following:    I have no idea why it is written with a supremum. I've spent hours pondering this, does anyone have enough of a background to help me with this? Thank you!
I accidentally changed /var owner/group to my username and then changed it back to root, but not all the /var folders' owners are root, so is there anyway to change back owner/group of files/folders to default state?  Or at least those files/folders that are created by packages? Say if I have a dropdown in a form and I have another nested class inside of this class . Now what's the best way to access this dropdown from the nested class? how to make a full backup of ubuntu server for another computer? I have a Ubuntu 15.10 server, which currently has a bunch of software installed on. Now, I want to make a full backup of everything there (including profiles, configs, etc...) on this computer (virtually on Parallels Desktop) for another physical computer which I've recently installed Ubuntu 15.10 server on it.  So how can I transfer this system completely into that computer? I tried PinguyBuilder and Systemback, but they were not what I wanted.  Considering that if there is a way, which would need not or at least a Internet connection (specially on physical computer) would be awesome.  Any help?  P.S: I know there are many topics for backup things, but they are not exactly for a non-gui server, or maybe I couldn't find what is suitable for me. I am running a web site design service for local small business owner. I want avoid legal issues on the images I use. Usually, the images found on Flickr are forbidden for commercial use. Where would be a normal channel to get pictures for commercial use with minimal cost? How can I validate that the picture I used has no legal risk? How can I propose a new site? Should I use a comma in this sentence? I am trying to teach myself punctuation rules. I have this sentence:     The Disney version generally considered both racist and sexist portrayed the female characters in stereotypical roles and presented ethnically diverse characters with stereotypical features.   I think the sentence needs a comma after sexist and before portrayed. I also think it needs a comma after roles because of what I have identified as a coordinating conjunction. I.e.:     The Disney version generally considered both racist and sexist, portrayed the female characters in stereotypical roles, and presented ethnically diverse characters with stereotypical features.   Did I punctuate the sentence correctly? Is this a coordinating conjunction? I'm trying to make a map using the Javascript API.  I want to use my own basemap, but I can't find the most simple code to do this.  I always see something like this:    function init() {     map = new esri.Map("mapDiv", {       basemap: "satellite",       center: [-97.395, 37.537],       zoom: 11     });   But I don't want to use the ArcGIS online basemaps.  What is the code to make a map service I am hosting my basemap? LaTeX code sniffer and/or beautifier? I'm looking for a LaTeX code sniffer and/or code beautifier, because I'm creating a CI server for my LaTeX books and I wanted a few things. :D Does $\sum_{n=1}^\infty \frac{\cos{(\sqrt{n})}}{n}$ converge? I am making a skydome and I have a texture hooked up with an emission shader for it, however, since the dome is blue it only emits blue light. Is there a way that I can have the whole sky illuminated and have the light reaching the rest of my scene be a different colour? Does the verb &quot;provide&quot; always have to be used with &quot;with&quot;? For example,  Can you provide me with some good examples? Can you provide me some good examples? Can you provide some good examples?  I suppose it's a transitive verb, isn't it? Moreover, is the following type of usage correct?  You should provide food for your dog before you go on vacation.  If you could give me some good examples regarding &quot;provide&quot; with different types of usage, I'd appreciate that. I covered hyperbolic trigonometric functions in a recent maths course. However I was never presented with any reasons as to why (or even if) they are useful.  Is there any good examples of their uses outside academia? Javascript infamous Loop issue? Could "them" mean "those"? Convert a string to an enum in C# If the second field of the /etc/shadow file is set to !!, does it mean that the account is disabled? Or does it mean that the account is active with no password assigned? How to rename multiple files sequentially from command line? How to rename file as below  AS1100801000002.RAW7AGS  AS1100801001008.RAW7AH4 AS1100801002001.RAW7AH9 AS1100801003002.RAW7AHE AS1100801004009.RAW7AHT AS1100801005002.RAW7AHY AS1100801010002.RAW7AJ3   to new name  AS1.txt AS2.txt AS3.txt AS4.txt AS5.txt AS6.txt AS7.txt What's the easiest way to figure out if a window is opened modally or not?  CLARIFICATION:  I open a window calling   myWindow.ShowDialog();   I have a footer with an "OK" &amp; "Cancel" button that I only want to show if the window is opened modally. Now I realize I can set a property by doing this:  myWindow.IsModal = true; myWindow.ShowDialog();   But I want the window itself to make that determination. I want to check in the Loaded event of the window whether or not it is modal.  UPDATE  The IsModal property doesn't actually exist in a WPF window. It's a property that I have created. ShowDialog() blocks the current thread.   I'm guessing I can determine if the Window is opened via ShowDialog() by checking if the current thread is blocked. How would I go about doing that? I have a list/queue of 200 commands that I need to run in a shell on a Linux server.   I only want to have a maximum of 10 processes running (from the queue) at once. Some processes will take a few seconds to complete, other processes will take much longer.   When a process finishes I want the next command to be "popped" from the queue and executed.  Does anyone have code to solve this problem?  Further elaboration:  There's 200 pieces of work that need to be done, in a queue of some sort. I want to have at most 10 pieces of work going on at once. When a thread finishes a piece of work it should ask the queue for the next piece of work. If there's no more work in the queue, the thread should die. When all the threads have died it means all the work has been done.  The actual problem I'm trying to solve is using imapsync to synchronize 200 mailboxes from an old mail server to a new mail server. Some users have large mailboxes and take a long time tto sync, others have very small mailboxes and sync quickly. Find all continuous functions $f$ satisfying   $$\int_0^xf=(f(x))^2+C$$ for some constant $C \neq 0$, assuming that $f$ has at most one $0$.  I have a question about the solution to this problem. It says that   Clearly $f^2$ is differentiable everywhere, its derivative at $x$ is $f(x)$ (I'm assuming that this is because the left hand side is differentiable, the right hand side must be differentiable as well). So $f$ is differentiable at $x$ whenever $f(x) \neq 0$, and  $$f(x)=2f(x)f'(x),$$ so $f'(x) = \frac{1}{2}$ at such points. Thus, $f= \frac{1}{2}x+b$ for some $b$ on any interval where it is non-zero; if $f$ has a zero, this gives two possible solutions, with two possible values of $b$, but since $f$ is assumed continuous, they must be the same. So we need $$\int_0^x(\frac{1}{2}t+b)dt=(\frac{1}{2}x+b)^2+C$$  so we must have $b=\sqrt{-C}$ or $-\sqrt{-C}$, leading to two solutions for $C \lt 0$.  I don't understand the bolded statements. First, how does the differentiability of $f^2$ guarantee that $f$ is differentiable, and why only at $x$ where $f(x) \neq 0$?  Next, why are there two possible solutions if $f$ has a zero, but since $f$ is continuous they must be the same?  Finally, does the last statement mean that if $C \gt 0$, then there is no solution, since we're restricted to real numbers here?  I would appreciate it if anyone answers my questions.