What is the distribution of (1-CDF)? We know that the cumulative distribution function (CDF) follows the $U[0,1]$ distribution. What is the distribution of (1-CDF)? Is it also follows the $U[0,1]$ ? (I believe it's true for the normal distribution, how about in general)  Thank you in advance.
proof that p-value is uniformly distributed when the null hypothesis is true this is a follow up to the following response:   the response makes sense if $P=F(T)$ but what if the hypothesis you're testing requires $P$ to be calculated differently for example $P=1-F(T)$ ?
I ran into this site:  But I can't find it on here:  Is it even an &quot;official&quot; Stack Exchange project? Is there an option to create and Opt-in a user in the same API call? I'll like to add this functionality to the autocomplete widget in Entityreference field to show node ID next to the titles in the dropdown list. The reason behind the idea is to differentiate between multiple nodes with same title.  Example:    This is a title (3) This is a title (2) This is a title (1)   I know the node ID is shown once a selection is made but I like to show it in the dropdown list in order to pick the right node quickly based on the node ID. Example of a finitely generated faithful torsion module over a commutative ring Can a finitely generated module $M$ over a commutative ring have $\operatorname{Ann}(x) \neq 0$ for all $x \in M$ while $\operatorname{Ann}(M) = 0$?  It's not difficult to show that there is no such module if the ring is a integral domain. For general, I guess the answer is yes. But I failed to find a desired example. I use to run  $s =~ s/[^[:print:]]//g;   on Perl to get rid of non printable characters.   In Python there's no POSIX regex classes, and I can't write [:print:] having it mean what I want. I know of no way in Python to detect if a character is printable or not.   What would you do?   EDIT: It has to support Unicode characters as well. The string.printable way will happily strip them out of the output.  curses.ascii.isprint will return false for any unicode character. Stripboard/veroboard/matrix board design software I'm prototyping a simple layout for a small project on matrix board, but figured there must be a better way than drawing it all out on paper. Are there any aimed at matrix board?  I've found the following software for stripboard, but nothing explicitly for matrix board:     Stripboard Magic (seems to be abandonware, but there's page about it )  Stripboard Editor Limited free version, designed to integrate well with     Any more I've missed? Any recommendations? Problem aligning overlapping corner points in Illustrator I am drawing some overlapping paths in Illustrator. However, some anchor points of different paths do not align correctly, they create some rugged corners. I tried to manually adjust the points with the direct selection tool but it is difficult to handle the corners.  Can anyone help me to fix the corners in the red circles? Today I downloaded Ubuntu for my laptop. It runs great from a bootable USB, but when I tried to install it, I got the following error message: The installer encountered an error copying files to the hard disk:  [Errno 5] Input/output error  This is often due to a faulty CD/DVD disk or drive, or a faulty hard    disk. It may help to clean the CD/DVD, to burn the CD/DVD at a lower   speed, to clean the CD/DVD drive lens (cleaning kits are often    available from electronics suppliers), to check whether the hard disk   is old and in need of replacement, or to move the system to a cooler   environment.     I tried everything to install it on my laptop including redownloading the Ubuntu ISO image, but nothing worked. Should north, south, east and west be capitalised? Should cardinal points be capitalised? Please give a reason why they should or should not. Is it possible to remove inline styles with jQuery? What is the difference between /sbin/nologin and /bin/false? I have often heard it recommended that a user account should be disabled by setting its shell to /bin/false. But, on my existing Linux systems, I see that a great number of existing accounts (all of them service accounts) have a shell of /sbin/nologin instead.  I see from the man page that /sbin/nologin prints a message to the user saying the account is disabled, and then exits. Presumably /bin/false would not print anything.  I also see that /sbin/nologin is listed in /etc/shells, while /bin/false is not.  The man page says that FTP will disable access for users with a shell not listed in /etc/shells and implies that other programs may do the same. Does that mean that somebody could FTP in with an account that has /sbin/nologin as its shell?  What is the difference here? Which one of these should I use to disable a user account, and in what circumstances? What other effects does a listing in /etc/shells have? Problem from Herstein on group theory The problem is:  If $G$ is a finite group with order not divisible by 3, and $(ab)^3=a^3b^3$ for all $a,b\in G$, then show that $G$ is abelian.  I have been trying this for a long time but not been able to make any progress. The only thing that I can think of is: $$ab\cdot ab\cdot ab=aaa\cdot bbb\implies(ba)^2=a^2b^2=aabb=(\text{TPT})abba.$$ Now, how can I prove the last equality? If I write $aabb=abb^{-1}abb$, then in order for the hypothesis to be correct, $b^{-1}abb=ba\implies ab^2=b^2a$. Where am I going wrong? What should I do? Number of normal subgroups of a non abelian group of order $21$... CSIR December $2013$ Question is to :  Find the number of Normal subgroups of a nonabelian group $G$ of order $21$ other than $\{e\}$ and $G$.  What I have done so far is :  As $|G|=21=3\cdot7$  we have :  No. of sylow $3$ subgroups $1+3k$ dividing $7$ leaving out possibilities $1$ or $7$  No. of sylow $7$ subgroups $1+7k$ dividing $3$ leaving out only possibilities $1$.  So, we have a unique sylow $7$ subgroup and so it is normal.  I remember somehow that any normal group should come from a normal sylow subgroup or something like that.  S0, I prefer to conclude there is only one Normal subgroup for a non abelian group of order $21$.  Please let me know if this is true and please help me to fill that gap :      I remember somehow that any normal group should come from a normal sylow subgroup or something like that.   Thank you. Center of a free product Let $A$ and $B$ be two groups and let $G=A*B$ be their free product. Suppose both $A$ and $B$ are nontrivial. I want now to prove that $G$ is infinite and that $Z(G)$ is trivial.  I think I can prove that $G$ is infinite using this argument: two reduced words of $A*B$ are equal if and only if they have the same length and the ith letter of the first word is the same as the ith letter of the second one. Hence one can find a reduced word of $G$ of length arbitrarily big (since we are sure it won't be equal to a shorter word). Do you think it works? Has anyone another suggestion?  On the other hand, I don't really have a clue for the second part except trying to analyze a long list of cases of reduced words and prove for each one that the only element with which they commute is the identity. Does anyone have a smarter idea?  Thanks in advance! If you want to buy a house but you also think value will drop… is there something you can do to alleviate the risk? Disclaimer: yours won't be fiscal advice. People involved will consult a professional before doing anything. This is just to gather some preliminary information.  Situation:   you want to buy a house or a flat, in UK you will get a mortgage in GBP, but you'd pay the down payment in EUR you think that there are fairly high chances that the value of houses in UK and GBP will drop the whole point of this question is actually buying the house/flat, renting is not an option by definition   What can you do to mitigate that risk? Convert JavaScript string in dot notation into an object reference Do conjugate priors just lead to a posterior that is a modification of the parameters of the prior? We know, for example, that the conjugate relationship between the classic beta-binomial is as follows:  \begin{align}  y &amp;∼ \mathcal{Bin}(n,\ θ)  \\  θ &amp;∼ \mathcal{Beta}(α,\ β)  \\ θ|y &amp;∼ \mathcal{Beta}(y + α,\  n − y + β) \end{align}  Notice how the posterior is just a change in parameterization compared to the prior. Is the posterior of conjugate priors just a change in parameters? We have our main BU (business unit) at the top of the tree, and one of the other BUs is TEST. In TEST we have created an Installed Package and in that installed package we have added a Server-to-Server API Integration. In the Access tab of that API Integration we've disabled the integration for the Parent BU, and have enabled it for the TEST BU.  When we make Rest API calls to the endpoint created in that API Integration we always get data from the "Main" BU, and not from the TEST BU.  If I create a contact that is available in both the Parent and TEST BU, but if I try to trigger an email based on a Triggered Send definition only the definitions created in the Parent BU are available and not the definitions from the TEST BU.  How can I access the data in the TEST BU from the Rest API? And why aren't the permissions preventing me from taking actions on the Parent BU? So all wizards get an invitation to Hogwarts at 11... How do they know whom to invite?  If a wizard is Muggle-born, then nobody would know about their existence.  Or do they register some weird magical stuff being done by them before 11? Why are my quotation marks causing an “unexpected token” error with this command? I need help with a specific command that I am using in a new game that I am creating inside of Minecraft. The command is:  /give @p sign 1 0 {BlockEntityTag:{Text1:"{"text":" [MF2]","color":"gold","clickEvent": {"action":"run_command","value":"tellraw @a [""{"text":"[MF2]  ","color":"gold"},{"selector":"@p","color":"dark_aqua"},{"text":" is now an admin of the server!","color":"white"}]"}}",Text3:"{"text":"Click to join Admin","color":"dark_aqua","clickEvent": {"action":"run_command","value":"scoreboard teams join admin @p"}}"},display: {Name:"Custom Sign"}}   If I take out the /tellraw command then the command works fine, but I need the command in there to announce to the game that a new admin has joined.  With the tellraw command, the error message is the following:  Data tag parsing failed: Unexpected token 't' at: text":" [MF2]","color":"gold","clickEvent":{"action":"run_command","value":"tellraw @a [""{"text":"[MF2] ","color":"gold"}, {"selector":"@p","color":"dark_aqua"},{"text":" is now an admin  of the server!","color":"white"}]"}}",Text3:"{"text":"Click to join Admin","color":"dark_aqua","clickEvent": {"action":"run_command","value":"scoreboard teams join admin @p"}}"   If anyone knows how to fix this, please let me know.