$Y\sim\operatorname{Poisson}(\lambda_2 = 15)$. Let $Z = X + Y$ . Compute $\operatorname{Corr}(X, Z)$.
$X\sim\mathrm{Poisson}(\lambda_1 = 5)$ and $Y\sim\mathrm{Poisson}(\lambda_2 = 15)$. Let $Z = X + Y$ . Compute $\mathrm{Corr}(X, Z)$.
Is a match forfeited if a player refuses to leave after being sent off? Prove by induction that for every $n \ge 0$ the term $2^{2n+1} - 9n^2 + 3n -2$ is divisible by $54$ Move data from regular partition to lvm I've read a bit about lvm and decided that I want to switch to using it. It seems like actually setting up lvm can be done from the debian installer, so I suppose that'll be easiest. What I'm not sure about is how to copy all of my files to the new system.   I would like to copy my whole system, not just my home directory or just my packages, I've messed around with a lot of stuff, to the point where I have no idea exactly where all of my config files live. The guides I've found on the internet seem to glaze over this step, just mentioning tools that can do it, not how to use them, i.e. use rsync. Instinct tells me I can't just rsync the root of my backup to the root of my lvm system, I'll copy over something important, like the lvm config files, but I'm not sure what exactly I need to exclude, while being sure not to exclude anything I might have changed. Any tips?  My planned steps, for clarity: I have a 1tb hdd and a 250gb ssd. I want to shrink the partition I have on the hdd, use the free space (I have enough) to make two new partitions, and dd my ssd and hdd partitions to those partitions as a backup. Then I want to wipe the ssd partition and hdd partition I'm currently using, and set up lvm on them (ideally with the debian installer for simplicity's sake, but maybe manually). And then I want to copy everything from the backup partitions to the new lvm partitions, somehow. And then wipe the backup partitions and either resize the existing lvm partitions to include the remaining space, or just make the remaining space another physical volume on lvm and add it that way. Short story, domed refuges Derived template-class access to base-class member-data Introduction to AdS/CFT What is the difference between the displace socket and a bump map? Aside from the fact that you can control the bump mapping per shader with a bump node, are there any differences between these materials?      As far  as I can tell, they are the same. Is the displacement socket just a convenience thing? Is there a performance advantage? Cardinal of quotient rings of gaussian integers. It is known that $\mathbb{Z}[i]$ is a PID and that $\mathbb{Z}[i]/(a+bi)\mathbb{Z}[i]$ is finite for all $(a,b) \in \mathbb{Z}^2\backslash \{(0,0)\}$.  My question :      Is there any result on the cardinal of  $\mathbb{Z}[i]/(a+bi)\mathbb{Z}[i]$ ? Upon the risk of being down voted as no MWE is present, but at the moment just trying to get some pointers. I updated my MiKTeX installation to the newest available version at the moment (MiKTeX-pdfTeX 4.1 (MiKTeX 20.12)) and now I get an error while building my documentation: Appendix D. (../html/examples/group/latex/refman_doc.tex (../html/examples/group/latex//gro up__group1.tex) [243] ! I can't write on file `../html/examples/group/latex//group__group2.aux'. \@include ...mmediate \openout \@partaux &quot;#1.aux&quot;                                                   \immediate \write \@partau... l.3 \include{group__group2}  Please type another output file name ! Emergency stop. \@include ...mmediate \openout \@partaux &quot;#1.aux&quot;                                                   \immediate \write \@partau... l.3 \include{group__group2}  *** (job aborted, file error in nonstop mode)  some small background:  Started normally with pdflatex doxygen_manual.tex in here is the statement: \subinputfrom{../html/examples/group/latex/}{refman_doc} and in this file again: \include{group__group2} as far as I know the disk is not full and the protections of the files and directories are OK as well  It looks like that now an attempt is made to write to the directory ../html/examples/group/latex/ whilst in the past the file was written to the current directory. I already tried -shell-escape and -enable-write18 (as well as --shell-escape and --enable-write18) but to no avail.  Any known changes in respect to writing the aux file? Any hints  edit I asked another question () with the details and MWE but that was closed with the reason that it was a duplicate of this one ... So I'm adding the information now here: In the question  asked about the problems I encountered due to an update of my MiKTeX distribution, but didn't take the time (at that moment) to create a MWE, so it didn't attract much response. I have the directory structure:  main  manual.tex   group  group__group2.tex refman_doc.tex    manual.tex \documentclass{book} \usepackage{import} \usepackage{hyperref}  \begin{document} \subinputfrom{../group}{refman_doc} \end{document}  group__group2.tex \hypertarget{group__group2}{}{The Second Group}  refman_doc.tex {Module Documentation} \include{group__group2}  When running in the directory main the command pdflatex manual.tex I get the error: ... (../group/../group/refman_doc.tex [1{C:/Users/User/AppData/Local/MiKTeX/2.9/pdf tex/config/pdftex.map}] ! I can't write on file `../group//group__group2.aux'. \@include ...mmediate \openout \@partaux &quot;#1.aux&quot;                                                   \immediate \write \@partau... l.2 \include{group__group2}  Please type another output file name:  but in a non interactive mode (the usual way to run. i.e. with \batchmode) one doesn't get an opportunity to specify the file and the generation crashes. As written in the original question adding options like -shell-escape and / or -enable-write18 didn't help.  Is there a solution for this problem?  edit 2 I did some further test. I replaced the \subinputfrom with an \input statement, although this worked for the limited example above it didn't work for my larger codebase as here (again just a limited view) we have in the refman_doc.tex {Module Documentation} \input{group__group1} \include{group__group2}  with the contents of group_group1.tex similar to group__group2.tex and the file is also parallel to group__group2.tex. This results in the error: (manual.out) (manual.out) (../group/refman_doc.tex  ! LaTeX Error: File `group__group1.tex' not found.  Type X to quit or &lt;RETURN&gt; to proceed, or enter new name. (Default extension: tex)  Enter file name: ! Emergency stop. &lt;read *&gt;  l.2 \input{group__group1}  !  ==&gt; Fatal error occurred, no output PDF file produced! theorem numbering: section counter but remove the section number Single word for floating dust visible in sunlight Is there a single word used in English for the visibility of dust particles floating in a stream of sunlight?     shutterstock.com What are: province, territory, protectorate, state...? Often a country will have regions called "provinces" or "states". Other times they are called "territories" and "protectorates".   Is there a generic term for these words?  Is there a full list of words that belong to this group?  What makes them different from each other? I'm having trouble with the exercise in the title, even with part (a), which asks to prove that if $X$ is a closed subset of $\mathbb{P}^n_k$ of dimension at least 1 and $H$ is a non-empty hypersurface, then $X$ and $H$ meet.   Following the hint, I've done the following: By assumption, $X$ is given by $V(I)$ for some homogenous prime ideal $I\subset k[x_0,\dots x_n]=:A$ and $H$ by $V(f)$ for some homogenous polynomial $f\in A$. We wish to prove that there is a homogenous prime ideal $\mathfrak{p}$ (that's not the irrelevant one) containing both $I$ and $f$.  Consider the affine cone $\mathrm{Spec}\ A/I$ of $X$ in $\mathrm{Spec}\ A$. Being homogenous, both $I$ and $f$ are contained in the ideal $(x_0,\dots x_n)$. By Krull's principal ideal theorem, every minimal prime ideal containing $f\mod I$ has codimension one. $X$ having dimension at least one implies that there are homogenous prime prime ideals $\mathfrak{q}\supsetneq \mathfrak{r}\supset I$. This implies that $(x_o,\dots x_n)$ has codimension at least two. Thus there are prime ideals containing $f\mod I$ that are contained in $(x_o,\dots x_n)$. However, I'd need to show that there are homogenous such prime ideals, right? I'd rather get hints than full solutions. Get rid of the question ban on Meta; suspend actively harmful users manually Carmichael number square free Show that if $n$ is a , then $n$ is a square-free.  I did this: Let $n= (p^t)(m)$  where $t &gt;1$. Then by modular property,  $$b^p= b \mod n , \,\, b^m= b \mod n$$ Above two equations are also true in$\mod p$, $\mod p^t$. But in$\mod m$, just $b^n=b \mod m$.  And I tried to use CRT But I couldn't.  I think that I've chosen wrong way I have a question regarding classification in general. Let $f$ be a classifier, which outputs a set of probabilities given some data D. Normally, one would say: well, if $P(c|D) &gt; 0.5$, we will assign a class 1, otherwise 0 (let this be a binary classification).   My question is, what if I find out, that if I classify the class as 1 also when the probabilities are larger than, for instance 0.2, and the classifier performs better. Is it legitimate to then use this new threshold when doing classification?  I would interpret the necessity for lower classification bound in the context of the data emitting a smaller signal; yet still significant for the classification problem.  I realize this is one way to do it. However, if this is not correct thinking of reducing the threshold, what would be some data transformations, which emphasize individual features in a similar manner, so that the threshold can remain at 0.5? Real world uses of hyperbolic trigonometric functions 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? My &quot;hat&quot; is shown twice in my answer, once in my sig, and again above. MacOS 10.14.6; Safari Version 14.0.2 (14610.3.7.1.10) "whatever" as pure determiner? My dictionaries and references define, and I've always thought of, one of the functions of the word whatever as a "relative determiner."  In a sentence like, "I will help you in whatever way is possible,"  inserting the relative pronoun "that" between "way" and  "is", or replacing "whatever" with "the" - a pure, non-relative determiner - (I reckon) renders it ungrammatical:     *I will help you in whatever way that is possible.   *I will help you in the way is possible.   However, I do often encounter utterances like the first one above, such as:     My hope and intent is to contribute in whatever way that I can.   I wish to be of service to the local communities in whatever way that is possible.   where "that" is used, and thus "whatever" can be replaced by "the" without  making the sentences ungrammatical (if they are grammatical to begin with):     My hope and intent is to contribute in the way that I can.   I wish to be of service to the local communities in the way that is possible.   Is this usage of "that" with "whatever" wrong, though colloquial? If a linear operator has an adjoint operator, it is bounded