I am trying to to get an intuitive understanding and feel for the difference and practical difference between the term consistent and asymptotically unbiased.  I know their mathematical/statistical definitions, but I'm looking for something intuitive.  To me, looking at their individual definitions, they almost seem to be the same thing.  I realize the difference must be subtle but I just don't see it. I'm try to visualize the differences, but just can't.  Can anyone help?
Does each imply the other? If not, does one imply the other? Why/why not?  This issue came up in response to a comment on an answer I posted .  Although google searching the relevant terms didn't produce anything that seemed particularly useful, I did notice  on the math stackexchange. However, I thought that this question was appropriate for this site too.  EDIT after reading the comments  Relative to the math.stackexchange answer I was after something more in depth, covering some of the issues dealt with in . Also, as I see it the math.stackexchange question shows that consistency doesn't imply asymptotically unbiasedness but doesn't explain much if anything about why. The OP there also takes for granted that asymptotic unbiasedness doesn't imply consistency, and thus the sole answerer so far doesn't address why this is.
Do the Manuals and Tomes allow you to exceed 20 in an ability score? And can they be stacked? I am looking at items like Manual of Bodily Health, Tome of Clear Thought, etc.  Quoting from Manual of Bodily Health     If you spend 48 hours ... your Constitution score increases by 2, as   does your maximum for that score.   This sounds to me like when you read the tome according to the instructions, you are then allowed to increase your CON up to a maximum of 22.     Is that a correct reading -- that these magic items allow a player to override the usual ability score maximum of 20? Probably, you were already at 20 when you read it, but if, say, you were at 18 and read it to bring your CON up to 20, could you then later increase your CON further via feats or ability score increases gained at certain levels? Can you read more than one book of the same type, to increase your maximum by an additional 2 points? I know some countries such as UK has the steering wheels of their cars on the right side. But as we can see, most of the Europian countries uses it at the opposite side. Since I used to drive a car with left-steering wheel I found it impossible to drive a car with right-steer!  Not curiosity, but I am trying to map if this issue is related to User Experience or not. Using swap space instead of RAM can drastically slow down a PC.  So why, when I have more than enough RAM available, does my Linux system (Arch) use the swap?  Checkout my conky output below:    Also, could this be the cause of speed and system-responsiveness issues I'm having?  Output of free -m :  $ free -m              total       used       free     shared    buffers     cached Mem:          1257       1004        252          0         51        778 -/+ buffers/cache:        174       1082 Swap:          502        144        357 "What kind of a person" vs. "what kind of person" Problem using atan in pgfplots Migrated question's answers can be upvoted twice by the same user was created on Server Fault, answered on Server Fault, I upvoted some of those answers on Server Fault, and then moved by consensus to Super User.  Now that the question is on Super User, I can upvote the same answers I previously upvoted on Server Fault. Studying the equation $\ln(x)- 1+ x^2=0$ How can I visualize the file system usage on Windows? How can I visualize which folders and files are taking up all of the space on my hard drive?  I'm getting some conflicting reports on the size of hard drive contents. Namely what is and isn't there and what folders are actually using the space.   I need to know which of the files or folders the culprits behind all this hidden bloat. Also there should be a print option to get it on paper. There are 100 ropes in a bag. In each step, two rope ends are picked at random, tied together and put back into a bag. The process is repeated until there are no free ends. What is the expected number of loops at the end of the process? Find all number $n\in \mathbb N$ such that $\varphi (n)=14$ Open Source Command Line Tools to Remove Hyperlinks in PDFs? Are there any Open Source Tools to Remove PDF links in Ubuntu.  I use PDFtk and i am not able to find any internal links in it. Due to the Internal links my python script that uses PyPdf to merge the PDF files into one file fails. I'm having a problem setting up a vhost on Apache 2.4, using CentOS 6.3.  This question seems to have been answered several times on this forum, but none of the solutions work for me.  Basically, I set up a vhost with a particular document root. When I attempt to access the site, I get a permissions error. But I have no problem if I use a different root.  More specifically, if I set the root to be /volume1/web/xxx, I get a 503 because of a permission problem on index.html.  But if I set it to be /volume1/web, the index.html comes up without a problem.  The details:   I set the persmissions on volume1, web, and xxx to 755. I set the permissions on the index.html files to 777. I copy the index.html file to both /volume1/web and /volume1/web/xxx, so that they have identical index files with identical permissions.   In httpd.conf, I set the VirtualHost options so that I can easily switch the document root by changing 2 comment marks  I have the following lines in the conf file:  NameVirtualHost *:80  &lt;VirtualHost *:80&gt;     ServerName localhost     #DocumentRoot /volume1/web     DocumentRoot /volume1/web/xxx      #&lt;Directory /volume1/web&gt;     &lt;Directory /volume1/web/xxx&gt;       Options Indexes FollowSymLinks Includes ExecCGI       AllowOverride All       Order Allow,Deny       Allow from all     &lt;/Directory&gt;      ErrorLog logs/localhost-error_log     CustomLog logs/localhost-access_log common &lt;/VirtualHost&gt;   These lines contain all the suggestions that worked for other people with the same problem.  What I get when I enter localhost in my browser depends on the document root.   If the root is /volume1/web, the index.html page comes up. if the root is /volume1/web/xxx, then I get a 503 error, and the apache error log has this line:  [Thu Jul 19 17:17:52 2012] [error] [client ::1] (13)Permission denied: access to /index.html denied   I also tried adding an index.php file to the directory. I then got permission denied messages for both the php file and the html file.  I also tried setting the user : group to apache : apache on the directories and files. That didn't help.  I've done everything I can think of to fix the permissions, to no avail.  Does anyone have an idea about what's happening here?  Thanks. If $X$ is compact and $T:X \to Y$ continuous and bijective, show that $T$ is homeomorphism. Let $X$ and $Y$ be metric spaces, $X$ compact, and $T:X \to Y$ bijective and continuous. Show that $T$ is a homeomorphism.   My attempt:  We need only show that $T^{-1}$ is continuous.  Let $M \subset Y$ be closed. Then, from the surjectiveness of $T$, there exists a $A \subset X$ such that $T(A)=M$. Since $M$ is closed, by the continuity of $T$, we must have that $A$ is closed.  Now $$T^{-1}(T(A))=T^{-1}(M)$$ i.e, $A=T^{-1}(M)$. Since $A$ and $M$ are closed, we must have that $T^{-1}$ is continuous.  My problem with this, however, is that I am not using the fact that $X$ is compact anywhere in the proof. Is there perhaps another way that I can show this, using the compactness of $X$?   Any hints will be appreciated. How can I redirect the user from one page to another using jQuery or pure JavaScript? On the usage of "the" article with acronyms and initialisms I've read  and  I know that  1. The article is often used with initials that are pronounced letter by letter (initialisms).  2. The article is often NOT used with initials that are pronounced as a word (acronyms).  I used 'often' because I'm not sure about possible exceptions.  In my field of study (Operations Research), initials are frequently used to represent optimization problems (e.g., the TSP). I discussed this point with my university supervisor who makes comments on my reports (English is not his native language). He responded that:  "What I learned from [...] was that whenever we use (specific) acronyms, we don't use 'the' when they are within a sentence, and we use 'the' when a sentence starts with them. For instance,  (i) The HCP is an NP-Complete problem.  (ii) We developed a new algorithm to solve HCP."  HCP stands for the Hamiltonian Cycle Problem. It is really confusing me because I do not know when to use and when not to use the article. For example, on , the author Jane Watson writes:     Use a definite article with an initialism if the spelled out term begins with “the” but is not covered in the initialism.   which implies that I should use the article with "HCP". What do you think? Are \( and \) preferable to dollar signs for math mode? I have an HP ProBook 450 G2. Every time I shut down the computer and turn it back on after a day, the battery level decreases by about 5%. I'm sure that the computer is shut down, not in sleep or hibernate. I removed the battery from laptop and after inserting it, the battery percentage does not change. I tried updating the BIOS, disabling wake on LAN in BIOS options, and calibrating the battery several times.  Is this drain normal? If not, is it a hardware failure or can I fix it with software? If we have two circles in the plane described by $(x_1, y_1, r_1)$ and $(x_2, y_2, r_2)$ we can determine if they are completely disjoint by simply:  $$(x_1 - x_2)^2 + (y_1 - y_2)^2 &lt; (r_1 + r_2)^2$$  Assume this is not the case, we now want to know if one completely overlaps the other.  (That is: if the second circles interior is a subset of the first circles interior.)  If $(x_1, y_1) = (x_2, y_2)$ than we can trivially compare radii, so lets assume their centers are distinct.  The way I have imagined is to create a parametric equation of the line that connects the two centers:  \begin{align} x_p(t) &amp;= x_1 + t(x_2 - x_1) \\ y_p(t) &amp;= y_1 + t(y_2 - y_1) \end{align}  Then we calculate the two line segments (represented as two pairs of t values) where the circles intersect this line.  One is a subset of the other if and only if the corresponding circles are subsets of each other.  Is there a simpler approach I am overlooking? Is there a free or open source library to read Excel files (.xls) directly from a C# program?   It does not need to be too fancy, just to select a worksheet and read the data as strings. So far, I've been using Export to Unicode text function of Excel, and parsing the resulting (tab-delimited) file, but I'd like to eliminate the manual step. Where is a good place to learn classical optics for high school competitions? I need to learn basic optics for a high school academic competition. Does anyone know any good places, preferably free and online, to learn the basics of optics, like lenses, angles of incidence, etc.? I can't seem to find an MIT OpenCourseWare course addressing the issue.