During my searches I've come to a strange position; The Probit definition in Wikipedia is simple; $$\operatorname{probit}(p) = \sqrt{2}\,\operatorname{erf}^{-1}(2p-1)$$ Then, I've come to a  that explains using  The probit $Y$ of the proportion $P$ is defined by; $$P(Y) = \frac{1}{\sqrt{2 \pi}} \int_{-\infty}^{Y-5} e^{-\frac{1}{2}u^2}du. $$ I've verified both using the Sagemath, but there is no relation that I can see between these two functions. Am I missing something? Are those the same (actually the inverse of each other)? Note: I'm trying to understand the probits on the concept of the $\text{LD}_{50}$.
If the Standard Normal PDF is $$f(x) = \frac{1}{\sqrt{2\pi}} e^{-x^2/2}$$  and the CDF is  $$F(x) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^x e^{-x^2/2}\mathrm{d}x\,,$$  how does this turn into an error function of $z$?
Chrome always quit when I click on the X button on a tab, without asking me anything!  Even when I close Chrome he do not alert me if I am willing to relay close it?   Many times it happened that accidentally I clicked on X button. Is there any built-in way to get the length of an iterable in python? For example, files, in Python, are iterable - they iterate over the lines in the file. I want to count the number of lines.   One quick way is to do this:  lines = len(list(open(fname)))   However, this loads the whole file into memory (at once). This rather defeats the purpose of an iterator (which only needs to keep the current line in memory).  This doesn't work:  lines = len(line for line in open(fname))   as generators don't have a length.  Is there any way to do this short of defining a count function?  def count(i):     c = 0     for el in i: c += 1     return c   To clarify, I understand that the whole file will have to be read! I just don't want it in memory all at once I plan to self-study linear algebra this summer. I am sorta already familiar with vectors, vector spaces and subspaces and I am really interested in everything about matrices (diagonalization, ...), linear maps and their matrix representation and eigenvectors and eigenvalues. I am looking for a book that handles every of the aforementioned topics in details. I also want to build a solid basis of the mathematical way of thinking to get ready to an exciting abstract algebra next semester, so my main aim is to work on proofs for somehow hard problems. I got Lang's "Intro. to Linear Algebra" and it is too easy, superficial.  Can you advise me a good book for all of the above? Please take into consideration that it is for self-study, so that it' gotta work on its own. Thanks. Why did Eve die with Maelon's data available? I saved Wrex in ME1, I saved Maelon's data in ME2, the import screen in ME3 confirmed this.    When I get to the missions on Tuchanka, I completed every one of the side missions before starting the mission where they take down the Reaper and distribute the genophage cure.  Then when I finally get to the lab, Mordin tells me that Eve has died.    Yet every site I've been to says that keeping the data allows her to live.  So why did she die? According with Mumford the answer is yes, but there are some obscure points in the proof.  We know that there exists a very ample line bundle on $A$ since every abelian variety is projective. Hence, via some corollaries of the Theorem of the Cube, we get an ample line bundle whose restriction to the kernel of $n_A$ is both the trivial bundle and very ample. This should imply that the dimension of $\ker n_A$ is $0$.  Furthermore, Mumford says that the fact that the dimension of the kernel is $0$ implies the surjectivity of $n_A$.  Is anybody able to clarify these two points to me?  Thanks in advance! A positive polynomial is the sum of two squares in $\mathbb{R}[X]$ Let $P\in\mathbb{R}[X]$ be a positive polynomial.  I want to show that there exists $A,B\in\mathbb{R}[X]$ so that $P=A^2+B^2$    $\displaystyle P=a\prod_{k=0}^q(x-a_k)\prod_{k=0}^{2p}(x-b_k)=a\prod_{k=0}^q(x-a_k)\prod_{k=0}^p(x^2-2\Re(b_k)+|b_k|^2)$ where $a$ is the leading coefficient, $a_k$ are the real rooks, $b_k$ are the complex roots.  What can i do now ? I know that the identity $(a^2+b^2)(c^2+d^2)=(ac-bd)^2+(ad+bc)^2$ should come in handy, but I can't figure out :  1) How to show that the product real roots is a square  2) How to use the above identity for the complex roots.  If I can solve those two points, then I can solve the problem. Print composer custom grid label problem In answer to  Klas Karlsson puts forward a solution to the problem of formatting print composer grid labels for projected maps.  I'm very weak on scripting, but in QGIS 2.14 I've tried to enter the text as shown in Klas's illustration, which generates error messages. In my case I'm working with a coordinate system that has a six-digit Easting and a six-digit Northing and I'm trying to get a result similar to that shown in Klas's picture (but with a six-digit Northing). Can anyone help me with this? "Series" – a noun of multitude similar to "lot", "majority", "percentage", "proportion"– verb agreement According to Garner's fourth edition  Though serving as a plural when the need arises, series is ordinarily a singular noun. But it is also a noun of multitude, so that phrases such as a series of things take a plural verb. However, the collocation there {has been - is} a series has predominated in print sources. Common nouns of multitude: lot, majority, mass, minority, multitude, percentage, proportion, variety.  However,  reads  When it has the singular sense of &quot;one set,&quot; it takes a singular verb, even when series is followed by of and a plural noun: A series of lectures is scheduled.  Are these dissimilar usages stylic advice? Secondly, the inversion after there also chooses singular elsewhere; why is it so?  When the verb precedes the noun percentage, a singular verb is required. That is, a higher percentage of them are, but there is a higher percentage of them. How to create a GUID / UUID I'm trying to create globally-unique identifiers in JavaScript.  I'm not sure what routines are available on all browsers, how &quot;random&quot; and seeded the built-in random number generator is, etc. The GUID / UUID should be at least 32 characters and should stay in the ASCII range to avoid trouble when passing them around. Is there console mode in Mac OS X? How to find a Java Memory Leak How do you find a memory leak in Java (using, for example, JHat)? I have tried to load the heap dump up in JHat to take a basic look. However, I do not understand how I am supposed to be able to find the root reference () or whatever it is called. Basically, I can tell that there are several hundred megabytes of hash table entries ([java.util.HashMap$Entry or something like that), but maps are used all over the place... Is there some way to search for large maps, or perhaps find general roots of large object trees?  [Edit] Ok, I've read the answers so far but let's just say I am a cheap bastard (meaning I am more interested in learning how to use JHat than to pay for JProfiler). Also, JHat is always available since it is part of the JDK. Unless of course there is no way with JHat but brute force, but I can't believe that can be the case.  Also, I do not think I will be able to actually modify (adding logging of all map sizes) and run it for long enough for me to notice the leak. PostgreSQL, SELECT from max id $\sum_{i=1}^n(a_i)\sum_{i=1}^n(\frac{1}{a_i})\ge n^2$ is what I want to prove, where $a_i&gt;0$ and I need to showwhen equality holds.  I have tried using Cauchy-Schwarz, where inside the sums I multiply each value by 1 to do it but it doesn't work out.  I have also done  $\sum_{i=1}^n(a_i)\sum_{i=1}^n(\frac{1}{a_i})=\sum_{i=1}^n \sum_{i=1}^n(\frac{a_i}{a_i})=\sum_{i=1}^n\sum_{i=1}^n(1)=\sum_{i=1}^n(n)=n^2$, but this proves an equality.  Am I not allowed to do the first step I did in my work? Javascipt component not coming render as pdf Follow up: instance control in Java without enum Notice: Undefined variable: logged in C:\xampp\htdocs\Site\Site\view_category.php How to get attention to a post on a child meta site If I want to draw people's attention to a post on a child meta site, how can I do that? I want to get people  over at Area 51 to see what they think of the idea, because it requires opinions from the community. However, posts on the discussion zone of Area 51 rarely get activity, so it seems like I'm out of luck, unless something is changed. And from the sounds of , it seems like this is a problem on all child metas.  That post is similar, but while it talks about increasing activity in general, I am talking about how to raise participation to an individual post; the equivalent of a bounty  I can't use bounties because reputation is the same.   Could there be another way of drawing attention to individual posts? $f : S^1 \to\mathbb R$ is continuous then $f(x)=f(-x)$ for some $x\in S^1$ Question is to prove :  $f : S^1 \to \mathbb R$ is continuous then $f(x)=f(-x)$ for some $x\in S^1$  I guess it would be helpful to use intermediate value theorem  Assuming $f(x)\neq f(-x)$ then given any $p\in (f(-x),f(x))$ (assuming $f(-x)&lt;f(x)$) there exists $y\in (-x, x)$ such that $f(y)=p$  I am not very sure of how to use this..   It would be helpful if someone can give some hint which would help me to solve this..  Thank you. If apostrophe + s is the acceptable way of denoting a genitive in English, is it possible that possessive pronouns, such as hers, ours and yours, started life as possessive adjectives with apostrophe + s?  E.g. her's, our's, your's, their's? Perhaps, even his' ? Its and my obviously stick out from this tempting pattern.  Is there any evidence that this might be the case, or is the 's completely unrelated? When a 0-1-matrix with exactly two 1’s on each column and on each row is non-degenerated? [1] Let $A$ be an $n\times n$ matrix with entries in the set $\{0,1\}$ which has exactly two ones in each column and two ones in each row.  Give necessary and sufficient conditions for the rank of $A$ to be $n$.