I am reading Introduction to Statistical Learning by James et al (freely available on their ). In the section the quote below is taken from, they illustrate how $t$-statistic is used to test the null hypothesis.  Now, I understand the definition of the $t$-statistic. But, I am having trouble wrapping my head around the definition of the $p$-value; particularly, in the quoted text below, which value are they exactly talking about?     Consequently, it is a simple matter to compute the probability of observing any value equal to $|t|$ or larger, assuming $\beta_1 = 0.$   In other words, I would like to know how, in Table 3.1, p.68, the $p$-value obtained?
After taking a statistics course and then trying to help fellow students, I noticed one subject that inspires much head-desk banging is interpreting the results of statistical hypothesis tests.  It seems that students easily learn how to perform the calculations required by a given test but get hung up on interpreting the results.  Many computerized tools report test results in terms of "p values" or "t values".  How would you explain the following points to college students taking their first course in statistics:   What does a "p-value" mean in relation to the hypothesis being tested?  Are there cases when one should be looking for a high p-value or a low p-value? What is the relationship between a p-value and a t-value?
Proper fstab entry to mount a samba share on boot? I am a little confused on the proper fstab entry for a samba share in Ubuntu 12.04     I can get the drive to mount manually by using:  sudo mount -t cifs //192.168.2.2/raid_drive /mnt/homeserver -o username=jon,password=password  So I tried putting this in fstab:  //192.168.2.2/raid_drive /mnt/homeserver cifs username=jon,password=password,iocharset=utf8,mode=0777,dir_mode=07‌​77 0 0  Which gives me this error in syslog:  kernel: [ 2217.925354] CIFS: Unknown mount option mode kernel: [ 2217.936345] CIFS VFS: default security mechanism requested.  The default security mechanism will be upgraded from ntlm to ntlmv2 in kernel release 3.3  This  says to use smbfs although I believe smbfs is deprecated?   What is a common fstab configuration for a samba share in Ubuntu 12.04?   EDIT:  Using the accepted answer below I was initially getting this error message (from dmesg):  [   45.520883] CIFS VFS: Error connecting to socket. Aborting operation [   45.520990] CIFS VFS: cifs_mount failed w/return code = -115   although it turns out this was due to network connectivity issues, and not related to improper fstab entry. Why are there holes in the icing? I tried to follow the new Blender 2.8 tutorial from Blender Guru.   When entering "Sculpting" with the icing there were suddenly alot of holes in it. Why is this? Proof of the Hockey-Stick Identity: $\sum\limits_{t=0}^n \binom tk = \binom{n+1}{k+1}$ After reading , the most popular answer use the identity $$\sum_{t=0}^n \binom{t}{k} = \binom{n+1}{k+1}.$$  What's the name of this identity? Is it the identity of the  modified.  How can we prove it? I tried by induction, but without success. Can we also prove it algebraically?  Thanks for your help.    EDIT 01 : This identity is known as the  because, on Pascal's triangle, when the addends represented in the summation and the sum itself are highlighted, a hockey-stick shape is revealed. How to solve the equation $\phi(n) = k$? Am not doing anything fancy, just trying to update a field on Contact in JS of LWC but getting this exception.  Uncaught TypeError: 'set' on proxy: trap returned falsish for property 'Name' throws at mydomain/auraFW/javascript/mhontaYdOya4Y_lBu7v9yg/aura_prod.js:2:27687  HTML Code:   &lt;template&gt;      &lt;template if:true={wiredContact}&gt;          {wiredContact.Name}          &lt;lightning-input value={wiredContact.Name} onchange={updateName}&gt;&lt;/lightning-input&gt;     &lt;/template&gt;  &lt;/template&gt;   JS:   import { LightningElement ,wire,track,api } from 'lwc'; import myContact from "@salesforce/apex/ContactController.fetchContact";  export default class Myrefreshapextest extends LightningElement {    @track wiredContact;   @wire (myContact)         fetchedContact({error, data}){             if(data){                 console.log(JSON.stringify(data));                 this.wiredContact = data;             }else if (error){                 console.log(error);             }     }      updateName (event){         console.log(JSON.stringify(event.detail.value));         console.log(JSON.stringify(this.wiredContact));         this.wiredContact.Name = event.detail.value;     }  }   Apex:  public class ContactController {      @AuraEnabled(cacheable=true)     public static Contact fetchContact(){         return [SELECT Id,Name FROM COntact LIMIT  1];     } }   On top of my head, am not doing anything wrong, anyone has idea what's wrong with my code?  When I print console.log(JSON.stringify(this.wiredContact)); I get old values so am pretty sure it exists.  I tried with @track and @api, but same response. Can anyone shed some light? Post Feedback link is broken I first noticed this a while back. But it has yet to resolve itself.  When I click on the  in the 10k tools, it hangs for a while.Then it gives me an error message: \documentclass{article} \usepackage{expl3} \ExplSyntaxOn \begin{document} \tl_to_str:n { testing _ things }  \par  \tl_set:Nn \l_tmpa_tl { testing _ things } \tl_to_str:N \l_tmpa_tl \end{document}   gives a strange result (testing ̇things).  How can I get testing_things?  I basically want verbatim content (with line breaking). number of distinct solution of Integral equation Total number of distinct $0\leq x\leq 1$ for which $\displaystyle \int_{0}^{x}\frac{t^2}{1+t^4}dt = 2x-1$   $\bf{My\; Try::}$ Given $\displaystyle \underbrace{\int_{0}^{x}\frac{t^2}{1+t^4}dt}_{\geq 0} = 2x-1\;,$ Where $0\leq x\leq 1$  So we get $\displaystyle x\geq \frac{1}{2}\;\;\;,$ Now  $\displaystyle \frac{d}{dx}\left\{\int_{0}^{x}\frac{t^2}{1+t^4}dt\right\} =\frac{d}{dx}(2x-1)$  So $$\frac{x^2}{1+x^4}=2\Rightarrow \underbrace{x^2+\frac{1}{x^2}}_{\geq 2} = \frac{1}{2}$$  So no real values of $x$  Is my solution is Right, If not then how can i solve it some short way, Thanks How to prove the property of the Lemoine point of a triangle? From Wolfram , I know there is a Lemoine point of triangle, also called symmedian point, the sum of squared distances of this point to all the three sides is algebraically minimum.    How to prove such a property? I need to compute the improper integral $$ \int_{-\infty}^{\infty}\frac{x^{2}}{\cosh\left(x\right)}\,{\rm d}x $$ using contour integration and possibly principal values.  Trying to approach this as I would normally approach evaluating an improper integral using contour integration doesn't work here, and doesn't really give me any clues as to how I should do it. This normal approach is namely evaluating the contour integral $$ \oint_{C}{\frac{z^2}{\cosh\left(z\right)}\mathrm{d}z} $$ using a semicircle in the upper-half plane centered at the origin, but the semicircular part of this contour integral does not vanish since $\cosh\left(z\right)$ has period $2\pi\mathrm{i}$ and there are infinitely-many poles of the integrand along the imaginary axis given by $-\pi\mathrm{i}/2 + 2n\pi\mathrm{i}$ and $\pi\mathrm{i}/2 + 2n\pi\mathrm{i}$ for $n \in \mathbb{Z}$. The residues of the integrand at these simple poles are $-\frac{1}{4}\mathrm{i}\pi^{2}\left(1 - 4n\right)^{2}$ and $\frac{1}{4}\mathrm{i}\left(4\pi n + \pi\right)^{2}$, so that even when we add up all of the poles, we have the sum $4\pi^{2}\mathrm{i}\sum_{n = 0}^{\infty}\,n$, which clearly diverges.  Any hints would be greatly appreciated. If I push or hit an object in space will it rotate or move along a straight line? If I push or hit an object in space (vacuum and no gravitation) in direction what is not going trough its centroid, will it rotate or move along in straight line?   I expect that on earth it will depend on what is less difficult for the object (rotation or linear movement). So the object will do some kind of combination of both movements (rotating and also moving along the direction of impulse or force).  But how could an object "decide" what to do in space, where is not resistance? biblatex and autonum don't work together biblatex and autonum don't seem to work together in the newest version. Consider the following MWE:  \documentclass{article} \usepackage[utf8]{inputenc} \usepackage[backend=biber]{biblatex} \usepackage{autonum}  \begin{document}  \end{document}   I get the following error messages:  0 File ended while scanning use of \ettl@for@do1 0 pdflatex: \pdfmatch: repetition-operator operand invalid pdfTeX warning: pdflatex: \pdfmatch: repetition-operator operand invalid)Runaway argument?{{\blx@bibdata@i {\blx@tempb }}\blx@bibfiles \eappto \blx@tempa {\blx@xml@comme   After commenting out either biblatex or autonum, the errors disappear. Compound Adjectives and -ed A colleague asked me this question, and I couldn't come up with an answer that satisfied him, so I'm wondering if anyone can help:  Why does a man with a short temper become a short-tempered man? In other words, why do you need the -ed at the end?  Are there any special rules for this? This is something I just realised I don't entirely know the answer to, so I'm going to ask it here as I think it's interesting.  In most non-scientific writing on depth of field, diagrams generally show camera and subjects as being perfectly parallel, e.g.    However, is this a more accurate representation of the focal plane?    Are there ways to optically alter the shape of the focal plane?  Note: Obviously these diagrams are two dimensional, but I'm assuming in the second diagram the shape would be spherical with the sensor at the center. Where to download Flash Player for offline installation? I can't find Flash Player download link which will give me the full EXE/MSI file, not the tiny downloader which downloads data from the internet.  What's the proper download site for this? What is the meaning of "build off of"? What is the meaning of "build off of"? I Googled it, but can't find any definition!  I encountered it in the sentence in a technical book. The sentence is:     For the application we will build, the todos example is the closest   fit, so we'll go ahead and build off of that example.   There is a link related to it I found by Google, But it didn't give the definition! Evidence for quantum gravity from gravitational waves The rumor spreads that .  I am far from being an experimentalist, but I want to know if there is any chance that the mentioned observations will reveal any experimental evidence for quantum gravity.  Personally, I feel like this is merely impossible as gravitational waves should propagate in agreement with classical General Relativity. But I might very well not see pitfalls if there are any.  UPDATE: by "evidence for quantum gravity" I mean experimental results which don't agree with predictions of General Relativity or its classical generalizations. They might be coming from string theory or loop gravity or from a completely different approach which we haven't discovered yet. I want to understand what are the chances that new physics will show up during the upcoming  gravitational wave observations.  Also, I expect gravitational waves to be in a highly coherent state, thus making the individual gravitons unobservable. Is this true? Pages: How to put a word between horizontal rules How can I make something that looks like this?  --------   Text   ---------  where the horizontal rules extend to the margin on either side? Just received ~70 unsolicited password reset mails from Super User, so abusive... Changing plurality in parentheses If a set of parentheses lies between a subject and its verb, and the parentheses contain an substitutive subject whose singularity/plurality disagrees with the original subject, whose singularity/plurality should be chosen for the verb?  In other words, in the following example, should "questions" (and its verb "are") be singular, or should they remain plural as shown?     Many (if not every) questions on this StackExchange are answered.   My intuition tells me that the two words in question should remain in plural forms, since the text in parentheses only interrupts the sentence (and the sentence would be grammatically incorrect if everything in parentheses were removed and the words were in singular form).  On the other hand, when read aloud (assuming one reads the text in parentheses), this has an uncomfortable sound to it, and I've seen others write in what would be the above example's singular-form case, so I'm curious to find out which is correct.  And, thinking about it, I suppose the same question would apply when commas are used in place of parentheses.