According to ,     A "blunt" support curve (one with a shallow maximum) would have a low   negative expected second derivative   In my mind, a blunt support curve has slow-changing slope, hence small second derivative, hence big negative expected second derivative (instead of small).  Where am I wrong in my thinking?
Suppose we have a random variable $X \sim f(x|\theta)$. If $\theta_0$ were the true parameter, the the likelihood function should be maximized and the derivative equal to zero. This is the basic principle behind the maximum likelihood estimator.   As I understand it, Fisher information is defined as   $$I(\theta) = \Bbb E \Bigg[\left(\frac{\partial}{\partial \theta}f(X|\theta)\right)^2\Bigg ]$$  Thus, if $\theta_0$ is the true parameter, $I(\theta) = 0$. But if it $\theta_0$ is not the true parameter, then we will have a larger amount of Fisher information.   my questions    Does Fisher information measure the "error" of a given MLE? In other words, doesn't the existence of positive Fisher information imply my MLE can't be ideal?  How does this definition of "information" differ from that used by Shannon? Why do we call it information?
Is $\langle1-i\rangle$ a maximal ideal in $\mathbb{Z}[i]$? I'm trying to show that $\langle1-i\rangle$ is a maximal ideal of $\mathbb{Z}[i]$.  I started by assuming there is some ideal $A$ that properly contains $\langle1-i\rangle$, and then I want to show that $1 \in A$, and then I will have that $A= \mathbb{Z}[i] $, so $\langle1-i\rangle$ is maximal.  Is this the right approach?  Thanks  Second Attempt: Because $\forall a+bi \in \mathbb{Z}[i]$, we have $a+bi = (a+b) -b(1-i)$, then we have $a+bi - (a+b) = -b(1-i) \in \langle1-i\rangle$, which implies $a+bi +\langle1-i\rangle = a+b +\langle1-i\rangle$.  So every coset is of the form $c +\langle1-i\rangle$, where $c\in \mathbb{R}$.  Furthermore, $-i(1-i)^2=2 \in \langle1-i\rangle$. Write $c = 2q + r$, where $q,r\in \mathbb{R}$ and $r=0,1$.  Then because $2 \in \langle1-i\rangle$, we have $2q\in \langle1-i\rangle$ and therefore $2q= 2q+r-r = c-r\in \langle1-i\rangle$, so $c+\langle1-i\rangle = r+\langle1-i\rangle$, and every coset is of the form $0 + \langle1-i\rangle$ or $1 +\langle1-i\rangle$. Thus, $1 +\langle1-i\rangle$ is the only nonzero element, and is invertible with itself as its inverse.  Thus, $\mathbb{Z}[i]/\langle1-i\rangle$ is a field with two elements, and by a theorem, $\langle1-i\rangle$ must be maximal.  Is this correct? Why doesn't the Go statement execute in parallel? Users with less than 50 reputation points cannot write comments on questions and answers that they don't own.  Why does this limit exist? But I want to contribute now. What should I do instead? But I can't write a good answer without more information! Shouldn't I be allowed to post comments if I have reputation on a different site? But I saw a new user posting a comment! How did they do it? Why do I need 50 reputation to comment on my own post?   See also:    in the Help Center "The following packages have been kept back:" Why and how do I solve it? UNetbootin is stuck in an "Automatic boot in 10 seconds" countdown loop I made a bootable Windows 7 USB using UNetbootin, and when I try to boot from the bootable USB and select the Default boot menu entry, it gets stuck at the UNetbootin boot menu and it keeps repeating an Automatic boot in 10 seconds... message in an endless countdown loop. Selecting Press [Tab] to edit options and editing the options has no effect. When I go back to the boot menu, it keeps repeating the same countdown loop.   I've tried redoing the UNetbootin extraction, but I still have the same issue. Edited vs emitted - why one t vs two t's Why does "edited" have one "t" and  and "emitted" has two? "Edit" and "emit" are so similar in spelling and pronunciation.  I keep wanting to type "editted" for some reason. How to determine the point of intersection of two lines? I have two lines say P1( 0, -1, 0, -1 ) and P2( -1, 0, 0, -1 ). Since I'm working in 2D, there is no Z component. The x,y,z components are normals and the w component is the distance from origin. I am not given the origin or any points on the line.  What method should I use to programmatically determine the point of intersection for these two lines? When is the graph of the divisor relation on $[n]$ planar? I'm reading page number 4 here. In particular the section where it deals with the case $p=\infty$, that is , showing that $L^{\infty}$ is complete.    Two questions:  1) Why is the convergence uniform? where it says "for $x \in N^{c}$ , $f_{n}$ is a Cauchy sequence of complex numbers. Thus $f_{n} \rightarrow f$ uniformly. Clearly we have pointwise convergence but why is it uniform?  2) I don't see why $||f_{n} - f||_{\infty} \rightarrow 0$. Can you please explain this step?  Thanks.  (3/2015) Edit: The original link appears to be broken.  seems to provide a similar (maybe even identical) proof to the one the OP talks about with slight notational differences. Split file into multiple small files, separate by the newline symbol Is there a utility that split file by newline symbol? e.g if a file contains the following lines,  aa bbb cccc   If I want to split it to 3 files, the desired output would be:  aa, bbb And cccc (in 3 different files)  I already checked the split command, it only cut file by file sizes, not what I want.  If I don't wrote a utility myself, is there any standard tool to use? Say person A and person B are having a discussion/argument.   Person A tells person B that his views are arrogant, or closed-minded, or some other derogatory adjective. But in fact it is person A's views that are arrogant, closed-minded, etc. Person B's views are usually the exact opposite of what person A is accusing him of.  This sort of situation happens a lot when discussing politics or religion, for example.  What do you call person A, for calling person B something that he himself is?  I guess, for the most part, person A doesn't actually realize that he is the one that the adjective applies to, and not person B. Maybe there is a different name if person A knows the adjective also applies to him. So,  Each of my polygons is a separate object. Their default normals point like this:   But their orientation or local axes are like so:   How can I make their local axes to be like so, but automatically?   I guess particles might be one solution for this exact case (if you emit new objects on top of the existing ones) but let's say the original objects are triangles and I wouldn't want to change their shape and pointing direction at all, only their local orientation axes, would that be possible?  Cheers! I'm a little confused about the following sentences. Could you please tell me which one(s) is/are correct?        The first and the second chapter are difficult.   The first and the second chapters are difficult.   The first and second chapters are difficult.   The first and second chapter are difficult.      I believe #1 &amp; #3 are correct, while #2 &amp; #4 are incorrect.  But when seeing the answers to the Quora question , I wonder why they say #2 is correct. How to install pygments on windows 7 When I run LaTeX file its gives error as  "! Package minted Error: You must have pygmentize installed to use this package", you must have pygments installed. when I go through minted documentation minted itself required pygments, so Tex friend How do I install this pygment, I don't know the procedure to install. Please guid me or any link pygement.exe file Why is there such a big difference between "Size" and "Size on disk"? What are the pros and cons of the leading Java HTML parsers? Are the limits $\lim\limits_{n\to \infty }\left|\frac{a_{n+1}}{a_n}\right|\,$ and $\lim\limits_{n\to \infty }\sqrt[n]{|a_n|}\,$ equal? Let consider the power series $$ \sum_{k=1}^\infty a_kx^k. $$ We know that it converges when  $$\lim_{n\to \infty }\sqrt[n]{|a_n|}|x|&lt; 1\quad\text{or}\quad |x|&lt; \frac{1}{\lim_{n\to \infty }\sqrt[n]{|a_n|}}$$  But D'Alembert test tells us that it converges if $$|x|&lt; \frac{1}{\lim_{n\to \infty }\left|\frac{a_{n+1}}{a_n}\right|},$$ so since the radius of convergence is unique, we should have that $$\lim_{n\to \infty }\sqrt[n]{|a_n|}=\lim_{n\to \infty }\left|\frac{a_{n+1}}{a_n}\right|.$$  I tried to prove it, but this result looks strange to me. So if it doesn't work always, how can we have those to limit as radius of convergence? I guess the equality of those two limit should be true most of the time.  So under what conditions is it true? Notify-send ignores timeout? Maybe I'm doing something wrong, but shouldn't the commands (run separately) notify-send -t 1 &quot;test&quot; notify-send -t 1000 &quot;test&quot; notify-send -t 10000 &quot;test&quot;  have different timeouts? The first being nearly instantaneous, the second taking 1 sec and the third 10 seconds? In all cases it seems to take about six seconds for me. Is there a way around this behaviour? As the developers label this as a &quot;feature&quot; instead of a bug, I would like some alternatives. How does gravity work on Star Wars ships? Inspired by the question , how does gravity work on the Millennium Falcon and other ships its size? The passengers are not strapped in and regularly move around just easily as they would on a planet with Earth's gravity.   The answer for the Death Star refers to gravity often being "coreward" (presumably taking advantage of the natural gravity an object of such substantial mass would have), but that doesn't apply for a small ship. So how is gravity accomplished? What's wrong with XKCD's Frequentists vs. Bayesians comic? makes fun of a frequentist statistician who derives an obviously wrong result.  However it seems to me that his reasoning is actually correct in the sense that it follows  the standard frequentist methodology.   So my question is "does he correctly apply the frequentist methodology?"    If no: what would be a correct frequentist inference in this scenario? How to integrate "prior knowledge" about the sun stability in the frequentist methodology? If yes: wtf? ;-)