Suppose that $X$ and $Y$ are independent random variables. Is $X + Y$ independent from $X$?  Intuitively I think it should be so -  because if information about $X$ gave information about $X + Y$, it should also give information about $Y$ by subtracting X - which then rephrases as, if $X$ and $Y$ are not independent, are $X + Y$ and $Y$ dependent? To answer this I would need to say something about $\sigma(X + Y)$ (in terms of $\sigma(X)$ and $\sigma(Y))$, but I am not sure how to do so.  Or is it false? I don't know.  Edit: Duplicate of
As asked in the title? Does the independence of two random variables $X$ and $Y$ imply the independence of $X$ and $X+Y$? If so, what's the easiest way to prove that?
Find the area of largest rectangle that can be inscribed in an ellipse The actual problem reads:      Find the area of the largest rectangle that can be inscribed in the ellipse    $$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1.$$   I got as far as coming up with the equation for the area to be $A=4xy$ but then when trying to find the derivative I don't think I'm doing it right. How to fix the weird surface in fluid object My machine was updated today to Ubuntu 16.04.2. However, the kernel is still "4.4.0-62-generic". What happened (it seemed that the principal advantage of the 16.04.2 version was the update of the kernel to 4.8) ? Do I have to make a fresh install ? Typical Japanese style anime art, it was a series.   It has been around for more than 6 years. I think it mixed fantasy and sci-fi. It was certainly not Isekai and it has no magic, it feels more like revered science. A boy gets a gem embedded into his arm after a terrorist attack and transforms into a white and orange humanoid being. There are more people able to transform into these beings. There is also a red flying ship with a dark yellow underbelly that throws boxes with parachutes. There is also this top-secret laboratory where the scientists study how to battle against the beings. There are some other flying ships of varying colors. If I remember correctly, the protagonist gets amnesia near the end of the plot. Boxplot interpretation: is it correct that a boxplot is missing a whisker? I have a data set that has customerID and daily visits. This dataset records the number of times customers visited the site in a day.   customerID   TotalVisits  1            6  2            17  3            20  4            25   Just to explore the data further, I tried plotting the TotalVisits values in a box plot. The plot doesn't seem to have a lower whisker. q1=1 and there are no values between q1 and  q1-1.5(IQR). The plot has q1, q2 and q3. The minimum value and q1 are the same.   Is this why the boxplot doesn't have the lower whisker? Could you please help me with the interpretation? Is it correct to draw a boxplot without any whiskers?  [I am new to the site and I am not able to post the image.] Why (and how) did using cat on binary files mess up the terminal? If I understand the cat manual correctly:       concatenate files and print on the standard output   cat will take files as argument and print them on standard output. What I don't get is if I use the command:    cat img.png &gt; copy.png   I will obtain 2 png files identical while if I just    cat img.png     I have all chance that my terminal get messed up and misinterpret what I type.     How's that possible?   Binary values are still binary data. Why it does not simply shows a series of 0 and 1 or the interpretation of those binary data in ASCII or whatever the encoding in terminal is?   Is this behavior also possible by cating a text file containing strange characters?   Should a mechanism to prevent this behavior  like try{}catch{} statement should be implemented? How do I get %LocalAppData% in c#? How to increase label size of OpenLayers plugin basemap layers? Formatting a float to ###.## (two decimals) I want to create a   How can I create a formfield with N fields, each 5 mm wide with separations like in the picture?    At the moment I use a workaround with a for loop, but this renders the code hard to maintain. Finally I need a function \formline{N}{cellwidth}{label}{value} to create the complete formfield and fill it with an optional value:   The following code is available on .   \documentclass[a4paper,11pt]{article} \usepackage[utf8]{inputenc} \usepackage{tikz} \usetikzlibrary{shapes}  \thispagestyle{empty} % no pagenumber. The form should be a stand alone macro... later.  \definecolor{SEPAOrange}{RGB}{254,213,161} \definecolor{SEPADOrange}{RGB}{253,185,19} \definecolor{SEPABlindcolor}{RGB}{255,0,0} \begin{document} \begin{tikzpicture}[x=1 mm, y=-1mm] \pgfmathsetmacro{\yh}{4.2333} % y heigth step defined as 1/6 inch =&gt; 1/6 * 25.4 mm = 4.2333 mm \pgfmathsetmacro{\xs}{9} % x start (own definition) \pgfmathsetmacro{\xe}{141.5} % x end (own definition) \pgfmathsetmacro{\widefield}{4.9859} % def: 134.62 mm / 27 \pgfmathsetmacro{\narrowfiels}{3.9594} % def: 134.62 mm/ 34  \filldraw[draw=black,color=SEPAOrange] (7.62, 4.5*\yh) rectangle (149.86-7.62,105.83-1); %orange background  \filldraw[draw=black,color=white] (\xs, 5*\yh) rectangle (\xe, 6.5*\yh -1.5); %Recepient 27 Char \foreach \x in {1,...,26} {  \draw[color=SEPAOrange, line width=0.3mm] (7.62 + \x*\widefield, 5*\yh ) -- (7.62 + \x*\widefield, 6.5*\yh);  \draw[color=SEPAOrange, line width=0.7mm] (7.62 + \x*\widefield, 5.8*\yh ) -- (7.62 + \x*\widefield, 6.5*\yh); }  \filldraw[draw=black,color=white] (\xs, 7*\yh) rectangle (\xe, 8.5*\yh -1.5); %IBAN 34 Char \foreach \x in {1,...,33}  \draw[color=SEPAOrange, line width=0.3mm] (7.62 + \x*4, 7*\yh ) -- (7.62 + \x*4, 8.5*\yh);  \filldraw[draw=black,color=white] (\xs, 9*\yh) rectangle (\xe, 10.5*\yh -1.5); %BIC \filldraw[draw=black,color=white] (\xe-12*5, 11*\yh) rectangle (\xe, 12.5*\yh -1.5); %Value 12 Char  \filldraw[draw=black,color=white] (\xs, 13*\yh) rectangle (\xe, 14.5*\yh -1.5); %Subject1 \filldraw[draw=black,color=white] (\xs, 15*\yh) rectangle (\xe, 16.5*\yh -1.5); %Subject2 \filldraw[draw=black,color=white] (\xs, 17*\yh) rectangle (\xe, 18.5*\yh -1.5); %Subject3  \filldraw[draw=black,color=white] (\xs, 19*\yh) rectangle (\xs+22*5, 20.5*\yh -1.5); % IBAN 22 Char  \filldraw[draw=black,color=white] (149.86-17.59, 19* \yh) rectangle (\xe, 20.5*\yh -1.5); % counter \filldraw[draw=black,color=white] (\xs, 21* \yh) rectangle (42.52, 24.5*\yh); % date \filldraw[draw=black,color=white] (42.52+5, 21*\yh) rectangle (149.86-17.59, 24.5*\yh); % signature  \draw[color=SEPADOrange] (0, 4.5 *\yh) --(149.86, 4.5*\yh); upper dark orange line \draw[color=SEPADOrange] (0, 20.5 *\yh) --(149.86, 20.5*\yh); lower dark orange line \draw[draw=black,color=black, line width=0.3mm] (0,0) rectangle (149.86,105.83); % black border %\draw[align=left] at (\yh,\yh) {SEPA-Überweisung};  \end{tikzpicture} \end{document} I have, not one but two microSD cards that my phone (Samsung Galaxy Young, Gingerbread OS) seem to have broken. One is 1GB and the other is 2GB. The 1GB one won't be formatted.  When I put the 1GB one into the computer the computer prompts for a formatting. I don't care for the content so I tried to format it, but to no avail; the format fails and I have no idea what to do to make it work again.  I tried using the SDformatter software, but it can't format the card as it is write protected. I'm googling to solve it but so far no success.  My computer OS is win7 if that's of any relevance. Is $\mathbb{Q}(\sqrt{2}) \cong \mathbb{Q}(\sqrt{3})$? How to automate SSH login with password? How to automate SSH login with password? I'm configuring my test VM, so heavy security is not considered. SSH chosen for acceptable security with minimal configuration.  ex)  echo password | ssh id@server   This doesn't work.  I remember I did this with some tricks somebody guided me, but I can't remember now the trick I used... I think this story dates from the 1950s, plus or minus a decade - I read it about 30-35 years ago in a (then) fairly old story collection. It involves explorers on a planet falling into a gelatinous object that dissolves most of their bodies except for their brains and nervous systems. About four of them fall in to the same creature, and they discover that by thinking about it they can grow limbs and other body parts. At first they try to fight each other, by growing arms so they can hit each other's brains - and one of them realises that growing a skull would be a good idea - but later they agree to grow legs and move the creature around co-operatively. I would love to identify this story. Any way to list similar commands? When you write the command name wrong, bash often does this:  septi@norbert:~$ good No command 'good' found, did you mean:  Command 'gold' from package 'binutils' (main)  Command 'gmod' from package 'gmod' (universe)  Command 'goo' from package 'goo' (universe)  Command 'god' from package 'god' (universe)  Command 'geod' from package 'proj-bin' (universe)  Command 'gord' from package 'scotch' (universe) good: command not found   Or sometimes it does this:  septi@norbert:~$ nftp No command 'nftp' found, but there are 23 similar ones nftp: command not found   Is there any way to ask bash to show these 23 similar commands for me? And, is there a way to show similar commands, including those that aren't yet installed, instead of running the application, ftp for example? Alternative version of the Final Value theorem for Laplace Transform I wanted to change my own password (as an admin) so I did the following command:  sudo passwd   and then it prompted for a password but when I tryed to relog, my password was not changed. I'm now wondering what password did I changed since it did prompted me to enter a password but I'm not sure what password did it changed exactly.  I know that if I do sudo passwd &lt;MY_USER&gt; it works, I'm just wondering without a user what happens.  Thank you Why is Euclid's proof on the infinitude of primes considered a proof? I've expressed Euclid's proof on the infinitude of primes on Mathematica:  f[x_] := Product[Prime[n], {n, 1, x}] + 1 TableForm[Table[{f[x], PrimeQ[f[x]]}, {x, 1, 20}]]   Which results in:  $\begin{array}{ll}  3 &amp; \text{True} \\  7 &amp; \text{True} \\  31 &amp; \text{True} \\  211 &amp; \text{True} \\  2311 &amp; \text{True} \\  30031 &amp; \text{False} \\  510511 &amp; \text{False} \\  9699691 &amp; \text{False} \\  223092871 &amp; \text{False} \\  6469693231 &amp; \text{False} \\  200560490131 &amp; \text{True} \\  7420738134811 &amp; \text{False} \\  304250263527211 &amp; \text{False} \\  13082761331670031 &amp; \text{False} \\  614889782588491411 &amp; \text{False} \\  32589158477190044731 &amp; \text{False} \\  1922760350154212639071 &amp; \text{False} \\  117288381359406970983271 &amp; \text{False} \\  7858321551080267055879091 &amp; \text{False} \\  557940830126698960967415391 &amp; \text{False} \\ \end{array}$  The proof flaws for all those values, how is it considered a proof then? I guess that there might be infinite prime numbers according to the proof, but what is the guarantee that at some point it won't fail indefinitely? Is it possible to prevent an NSURLRequest from caching data or remove cached data following a request? On iPhone, I perform a HTTP request using NSURLRequest for a chunk of data. Object allocation spikes and I assign the data accordingly. When I finish with the data, I free it up accordingly - however instruments doesn't show any data to have been freed!  My theory is that by default HTTP requests are cached, however - I don't want my iPhone app to cache this data.   Is there a way to clear this cache after a request or prevent any data from being cached in the first place?  I've tried using all the cache policies documented a little like below:  NSMutableURLRequest *theRequest = [NSMutableURLRequest requestWithURL:[NSURL URLWithString:url]]; theRequest.cachePolicy = NSURLRequestReloadIgnoringLocalCacheData;   but nothing seems to free up the memory! How should I interpret this residual plot? I am unable to interpret this graph. My dependent variable is total number of movie tickets that will be sold for a show. The independent variables are the number of days left before the show, seasonality dummy variables (day of week, month of year, holiday), price, tickets sold till date, movie rating, movie type (thriller, comedy, etc., as dummies). Also, please note that movie hall's capacity is fixed. That is, it can host maximum of x number of people only. I am creating a linear regression solution and it's not fitting my test data. So I thought of starting with regression diagnostics. The data are from a single movie hall for which I want to predict demand.  The is a multivariate dataset. For every date, there are 90 duplicate rows, representing days before the show. So, for 1 Jan 2016 there are 90 records. There is a 'lead_time' variable which gives me number of days before the show. So for 1 Jan 2016, if lead_time has value 5, it means it will have tickets sold until 5 days before the show date. In the dependent variable, total tickets sold, I will have the same value 90 times.  Also, as a side remark, is there any book that explains how to interpret residual plot and improve model afterwards?