How to make sure if the residuals are normally distributed?
Regression - How do I know if my residuals are normally distributed?
Where in the registry does Windows store with which program to open certain file types? After installing Adobe PDF reader, it opens files with the .PDF file extension. Ones' default web browser opens .html files and notepad opens .txt files, etc.  Where exactly in the registry are these filetype - program associations stored in the registry?   In other words, how does Windows know with which software/program it must open a certain file(type)? Generalized Pell equation $x^2-2y^2=49$ Why is sudoers NOPASSWD option not working? Computing $ \lim_{n\rightarrow \infty}\left(\frac{1^n+2^n+\cdots \cdots +n^n}{n^n}\right)$ -Bash command not found appearing every time I start terminal every time I start my terminal, it always says "-bash:  .: command not found" twice.  Does anyone know how I can get rid of that? An increasing number of funding organizations require publications on the research that they fund to be open access, i.e. available to the public without having to subscribe to a journal or pay a fee. Does anybody know where I can find a list of journals/publishers that do not allow material that they publish to be published this way? A very basic ring theory question, which I am not able to solve. How does one show that    $\mathbb{Z}[i]/(3-i) \cong \mathbb{Z}/10\mathbb{Z}$. Extending the result: $\mathbb{Z}[i]/(a-ib) \cong \mathbb{Z}/(a^{2}+b^{2})\mathbb{Z}$, if $a,b$ are relatively prime.   My attempt was to define a map, $\varphi:\mathbb{Z}[i] \to \mathbb{Z}/10\mathbb{Z}$ and show that the kernel is the ideal generated by $\langle{3-i\rangle}$. But I couldn't think of such a map. Anyhow, any ideas would be helpful. I'm trying to solve this problem from Hatcher 3.3.24.  Let $M$ be a closed connected 3-manifold, and write $H_1(M, \mathbb{Z})$ as $\mathbb{Z^r} \oplus T$ where $T$ is torsion. Show that $H_2(M, \mathbb{Z})$ is $\mathbb{Z^r}$ if $M$ is orientable or $\mathbb{Z^{r-1}} \oplus \mathbb{Z_2}$ if $M$ is not orientable. In particular $r \geq 1$ if $M$ is not orientable. Using exercise 6 construct examples showing there are no other restrictions on the homology groups of closed 3-manifolds. (In the nonorientable case consider the manifold $N$ obtained from $S^2 \times I$ by identifying $S^2 \times \{0\}$ with $S^2 \times \{1\}$ via a reflection of $S^2$.)  I think I've solved the first part, here's my proof:   First note the following theorem: If $M$ is a closed connected and orientable n-manifold then $H_n(M, \mathbb{Z}) = \mathbb{Z}$ and $Tors(H_{n-1}(M, \mathbb{Z})) = 0$. If nonorientable, then $H_n(M, \mathbb{Z}) = 0$, $Tors(H_{n-1}(M, \mathbb{Z})) = \mathbb{Z_2}$.  Now note by Poincare duality and UCT we have that $H_2(M) \cong H^1(M) \cong \mathbb{Z^r} \oplus T_0 \cong \mathbb{Z^r}$.   In the nonorientable case consider the exact sequence:  $0 \longrightarrow H_2(M) \longrightarrow H_1(M) \longrightarrow H_0(M) \longrightarrow 0$  But we know $H_1(M) = \mathbb{Z^r} \oplus Z_2$ from the earlier theorem and $H_0(M) = \mathbb{Z}$.   Therefore $H_2(M) \cong ker(\mathbb{Z^r} \oplus Z_2 \rightarrow \mathbb{Z}) \cong \mathbb{Z^{r-1}} \oplus \mathbb{Z_2}$.   For the rest of the question I'm quite lost. How to deal with SettingWithCopyWarning in Pandas Fastest way to try all passwords Suppose you have a computer with a password of length $k$ in an alphabet of $n$ letters.  You can write an arbitrarly long word and the computer will try all the subwords of $k$ consecutive letters. What is the smallest word that contains all combinations of $k$ letters as subword? (i.e. the fastest way to hack the computer :) )  The smallest word that contains $n^k$ subwords of size $k$ has length $k-1+n^k$ and based on some easy cases, we would like to prove that it is in fact possible to find a word of such length that contains all possible passwords. The problem can be translated into a problem in graph theory, by taking as vertices all words of length $k$.  We tried $k=2$, where you can prove the conjecture by induction. For $n=2$ and small $k$ it also works. How to get the type of T from a member of a generic class or method Let's say I have a generic member in a class or method, like so: public class Foo&lt;T&gt; {     public List&lt;T&gt; Bar { get; set; }          public void Baz()     {         // get type of T     }    }  When I instantiate the class, the T becomes MyTypeObject1, so the class has a generic list property: List&lt;MyTypeObject1&gt;. The same applies to a generic method in a non-generic class: public class Foo {     public void Bar&lt;T&gt;()     {         var baz = new List&lt;T&gt;();                  // get type of T     } }  I would like to know what type of objects the list of my class contains. So what type of T does the list property called Bar or the local variable baz contain? I cannot do Bar[0].GetType(), because the list might contain zero elements. How can I do it? Can I live in the UK for a long time through repeat visits? I had recently entered the UK without a visa to be with my partner, from 21 July 2016 until 16 December 2016. I hope to return on the 9th of January. We don't meet the income requirement for a Spouse visa. I recently applied to university, and got in, and was intending to return to the UK on a student visa, but my university did not tell me about maintenance fees and my loan wasn't large enough to cover it all, so my visa would have been denied.  Now, I am hoping to attend university in the next semester, and therefore return to the US to apply for that visa. Do you think that if I try to return to the UK without a visa, I will be turned away?  I won't be working or studying during this time, however, I'm afraid that they'll consider it living in the UK illegally; I don't have a criminal record or anything like that. How can I pad a value with leading zeros? I've found  many queries to check edit counts, and I get different results for each one. Which one is the most accurate and up-to-date query? Or is there any way to see the edit count in stats? Cannot Delete Item "Could Not Find This Item" issue A friend sent a long a file (a .rar) he wanted me to check out for him before he installed it.  I downloaded it and unrared it with no problems, but it was full of .exe's instead of the intended contents (fonts) so I advised him to delete it immediately and not use.  I then proceeded to do the same, but the folder simply will not delete. Oddly the files went fine, and I never ran anything, but this is what I'm seeing:   Could not find this item  This is no longer located in C:\Users\This_User\Desktop. verify the item's location and try again.   I've tried the following things with no help:   Using "Unlocker" to Unlock and delete Using move on reboot and rebooting Using PendMoves (from sysinternals) and rebooting Elevating a cmd line, doing a dir /x to get the short name of the folder, and then del 'shortna~1' Moving the folder to a new folder and then trying to delete the parent folder   I'm on Windows 7 RTM, very fresh install. Any thoughts?  Update: Just to confirm, I've run Hijack this and half a dozen other malware detectors, and everything came back clean (no extra processes, no other obvious badness). Rebooting in safe mode didn't help either. I am going to start a phd at the US with an F1 visa. University told me that I could enter the US only 30 days before the date on I-20. Since English is not my first language (and this would be a big change in my life) I would like to go there by June.  The thing is that I have an European passport with a valid ESTA. My plan would be to arrive with this passport, stay 4-6 weeks , go to Canada for a short vacation (maybe flight maybe by land) and come back to the USA with F1 visa.  I have two questions about this:  1) is this possible?   2) If yes, how could I justify knowing I will lose my come-back flight during my first entry? (I would purchase round trip because one-way are too expensive, probably with less than 90 days difference) Should I ask questions I already know the answer to and answer them myself? Finding center and radius of circumcircle Find the center and radius of the circle which circumscribes the triangle with (complex) vertices $a_1,a_2,a_3$. Express the result in symmetric form.   I'm not sure where to start in this question. The circumcenter is the intersection of the perpendicular bisectors, but I don't know how to calculate the line equation of the perpendicular bisectors yet. As for the radius, after we find the circumcenter $c$ we can calculate it using $|c-a_1|$ (or $|c-a_2|$ or $|c-a_3|$; all three should be equal.) So how can I calculate the circumcenter? How to prove that it is a group? I'm looking for a way to insert a &lt;style&gt; tag into an HTML page with JavaScript.  The best way I found so far:  var divNode = document.createElement("div"); divNode.innerHTML = "&lt;br&gt;&lt;style&gt;h1 { background: red; }&lt;/style&gt;"; document.body.appendChild(divNode);   This works in Firefox, Opera and Internet Explorer but not in Google Chrome. Also it's a bit ugly with the &lt;br&gt; in front for IE.  Does anyone know of a way to create a &lt;style&gt; tag that   Is nicer Works with Chrome?   Or maybe   This is a non-standard thing I should avoid Three working browsers are great and who uses Chrome anyway?