Correlation between two constant variables using the different approaches
What is the correlation if the standard deviation of one variable is 0?
What does the notation like 8.6e-28 mean? What is the 'e' for? I have a problem with the interpretation of a test result in which the p-value is 8.6e-28. How should it be interpreted? What is the e for?  Specifically, I used White's Test for the homoscedasticity assumption of a linear regression:  White's general test statistic :  150.0535  Chi-sq( 9)  P-value =  8.6e-28 change color of pgfplot bar plot I want to plot two bar plots next to each other. This works without a problem. However both use the first color defined in a pre or selfdefined colorseries. I tried to modify the color manually in the plot, but the color and fill definitions have no effect:  \documentclass[border=5mm]{standalone} \usepackage{pgfplots, pgfplotstable}  \begin{document}  \pgfplotstableread[header=false, col sep=comma]{  1, first item 5, second item }\datatable  \begin{tikzpicture}   \begin{axis}[             ,xbar     ,bar width=2ex, y=3ex     ,enlarge y limits={abs=0.75}     ,ytick={data} % (\empty,data,{coordinate list})     ,yticklabels from table={\datatable}{1}   ]   \addplot table [     ,red!20!black,fill=red!80!white,     y expr=-\coordindex, % Use negative coordinate index as y coordinate     x index=0 % Use first column as x coordinate   ] {\datatable};   \end{axis} \end{tikzpicture}  \end{document}   The plot is still in the default blue. When I open nautilus does not open the left bar where it says computer and down markers such as music, documents, videos, downloads. I reinstalled nautilus from the synaptic package manager but nothing happened. What I can do to make that bar visible again? I recently got the book "selected problems in real analysis", and I'm stuck solving the very first problem  $(u_n)$ is a binary sequence iff it only contains $0$ and $1$ in the sequence  Let $A$ be the set of all binary sequences  I have to prove that $A$ and ${2}^{\mathbb{N}}$ have the same cardinality, that is to say there exists a 1-1 function from one set to another  I've thought about maybe considering integers as base-2 numbers  Thanks for your help Does Airplane Mode allow GPS location to pass through? This is what I saw when my plane was taxing to the runway at CDG:     Airplane mode was on and all other transmissions (except Location), including WiFi, mobile data, NFC and Bluetooth were off.  Location was not manually turned on by me, after I enabled Airplane Mode. It remained turned on.  What am I missing? Is GPS now so widely accepted on-board planes that Android changed its configuration to let this kind of signal/communication to pass through Airplane mode "block"?  I believe that  isn't a duplicate, because at that time (2016) Location was generally "included" in Airplane mode and was turned off by enabling it. Floating point comparison What does the Y capacitor in a SMPS do? What's the use of a decoupling capacitor near a reservoir capacitor? I've seen some circuits where a decoupling capacitor is used as well as a reservoir capacitor, like this (C4 and C5):    I've read about  and for me it looks as if they are meant to remove small fluctuations in the supply voltage. Then I thought - wasn't that the purpose of a  as well? Why wouldn't the reservoir capacitor be able to filter out the small fluctuations, if it is able to filter out the large fluctuations?  So I feel like I have a basic misunderstanding here. What is the purpose of a decoupling capacitor next to a reservoir capacitor, when we assume we place both equally near to the power consuming part? Or is the only advantage of the decoupling capacitor that it is smaller and can therefore be easily placed more near to the power consuming part? Let $X \ge 0$.  Show  \begin{align} \lim_{y\to\infty} y\,\Bbb{E}\left[ \frac1X \cdot1_{X&gt;y} \right] &amp;= 0 \quad\text{and} \\ \lim_{y \downarrow 0} y\,\Bbb{E}\left[ \frac1X \cdot1_{X&gt;y} \right] &amp;= 0. \end{align}  N.B.: The author doesn't assume $\Bbb{E}[1/X] &lt; \infty$.    My try:  Since the expectation appears on the RHS of Markov's inequality, I don't think this inequality can be applied to solve this question.  $$ \begin{aligned} y\,\Bbb{E}\left[ \frac1X \cdot1_{X&gt;y} \right] &amp;= \Bbb{E}\left[ \frac{y}{X} \cdot1_{X&gt;y} \right] \\ &amp;&lt; \Bbb{E}\left[ 1 \cdot1_{X&gt;y} \right] \\ &amp;= \Bbb{P}(X &gt; y) \\ &amp;\xrightarrow[y\to0]{} \Bbb{P}(X \ge 0) = 1 \end{aligned} \tag1 \label1 $$  For the first part $y \to \infty$, I apply Markov's inequality at the row $\Bbb{P}(X &gt; y)$ in \eqref{1}, so that $$\Bbb{P}(X &gt; y) \le \frac{\Bbb{E}[X]}{y} \xrightarrow[y\to\infty]{} 0?$$ But I don't have $\Bbb{E}[X] &lt; \infty$.  Thanks for any help. GPS PPS signal corresponds to data time? I currently have an Adafruit Ultimate GPS connected to an Arduino that outputing GPS data (nmea sentences) once per second.  There is also a pin on the GPS outputting 1 PPS signal.    My question is whether the pulse of the PPS suppose to match the time that the GPS data is coming in i.e are they are coming in at the same time?    Also does PPS pulse come in at the beginning of a UTC second or is it random and simply once a second? Why are my SVG imports so small? Remove Punctuation When Checking for Duplicate Titled Questions I recently saw a question titled "" (10k+ users only). I thought, "surely someone has asked this question before", and began looking for a duplicate.  is a question with the exact same title, just with a little different punctuation and casing. It was "Jquery vs Javascript" and "jQuery vs. Javascript?". The only difference being the ., ?, and the casing.  Since we now , I propose that when checking for questions with duplicate names, certain punctuation be striped out to prevent the duplicate from occurring in the first place.  As pointed out in the comments, if isn't already, white-space and non-printable characters may want to be removed for duplicate detection as well. Windows Active Directory naming best practices? This is a  about Active Directory domain naming.   After experimenting with Windows domains and domain controllers in a virtual environment, I've realized that having an active directory domain named identically to a DNS domain is bad idea (Meaning that having example.com as an Active Directory name is no good when we have the example.com domain name registered for use as our website).   , but I'm still not sure about what other rules there are around naming Active Directory domains.  Are there any best practices on what an Active Directory name should or shouldn't be? Is it possible to have site-specific badges? Apache doesn't log remoteIP when RemoteIPHeader X-Forwarded-For is present Where has all the RAM gone? I edited my mesh changing the number of vertices after adding shapekeys, and it get totally messed up when the shapekeys are on. Is there a way to solve this problem without remake the shapekeys all again!? What is the purpose of the EBP frame pointer register? I'm a beginner in assembly language and have noticed that the x86 code emitted by compilers usually keeps the frame pointer around even in release/optimized mode when it could use the EBP register for something else.  I understand why the frame pointer might make code easier to debug, and might be necessary if alloca() is called within a function.  However, x86 has very few registers and using two of them to hold the location of the stack frame when one would suffice just doesn't make sense to me.  Why is omitting the frame pointer considered a bad idea even in optimized/release builds? It is currently said that MD5 is partially unsafe. Taking this into consideration, I'd like to know which mechanism to use for password protection.  This question,   suggests that hashing multiple times may be a good idea, whereas  suggests using salt.  I'm using PHP. I want a safe and fast password encryption system. Hashing a password a million times may be safer, but also slower. How to achieve a good balance between speed and safety? Also, I'd prefer the result to have a constant number of characters.   The hashing mechanism must be available in PHP It must be safe It can use salt (in this case, are all salts equally good? Is there any way to generate good salts?)   Also, should I store two fields in the database (one using MD5 and another one using SHA, for example)? Would it make it safer or unsafer?  In case I wasn't clear enough, I want to know which hashing function(s) to use and how to pick a good salt in order to have a safe and fast password protection mechanism.  Related questions that don't quite cover my question: Reserved words as names or identifiers