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I can follow the proofs in which the asymptotic normal-distribution of a maximum likelihood estimator $\tilde{\theta}_n$ is derived.   however, does this already imply that the maximum likelihood estimates are asymptotically unbiased, i.e. do we have $$E(\tilde{\theta}_n) \to \theta \text{ as } n \to \infty?$$  Since I am aware that in general it is not true that convergence in distribution implies convergence in moments, an explanation would be nice.  The result is often stated e.g.  as "...it means that the bias of the maximum likelihood estimator is equal to zero up to the order $n^{-1/2}$")  1.) Are  some kind of regularity conditions from the mle theory used to establish this result?  2.) Or is a $\sqrt{n}$-convergence of an estimator (to a normal distribution) in general already enough to establish convergence of its moments?  Note: the Wikipedia article mentions Cox, David R.; Snell, E. Joyce (1968).  , as a source where the order of the bias is derived (formula (12) or (20)).   However in this paper I can't follow the arguments 100%, since their Taylor approximation of $L'(\widehat{\beta})$ is lacking the remainder term. What is the argument used here to discard it completely? 1N5819-E3/73  1N5819-E3/53 1N5819-E3/54   the first one is 4x cheaper than the last, why ?  aren't they all the same ? I'm basically searching for the opposite of putting all your eggs in one basket, where the risk is total failure because you did not hedge your efforts. I'm searching for a phrase that encompasses splitting your efforts and evokes the prospect of failing at both. A bird in the hand is worth two in the bush also encompasses a sense of having focused your efforts, but only alludes to total failure. To satisfy the criteria, the phrase must cover:  attempting two things (or multiple iterations of one thing) both of which you might succeed at, if you addressed them serially but both of which you fail at because you address them in parallel  Here are the idioms/phrases that do not sufficiently cover the idea and why:  &quot;A servant to two masters&quot;  This has the sense of competing priorities, but not the sense of failing to achieve your goals.  &quot;Jack of all trades. Master of none.&quot;  The sense is insufficiently pejorative. Being a jack-of-all-trades can be seen as an advantage; I'm trying to focus on the lack of mastery.  &quot;The man who fancied himself a wit, and was half-right.&quot;  From Christopher Hitchens. Hilarious, but lacking the sense of split effort between two things.  &quot;Walking and chewing gum at the same time.&quot;  An idiom for multi-tasking, not for failing to multi-task. Edit Addressing a few suggestions and another one that occurred to me:  &quot;Hedging your bets&quot; or &quot;Betting against yourself&quot;  In this case, you cannot win both bets, but you will almost certainly win one. You limit your upside, but also limit your risk. I'm looking in particular for total, catastrophic failure due to split attention/effort.  &quot;Can't walk and chew gum at the same time&quot;  Failing to do two fairly simple things that most everyone can do, not failing at two hard things because you tried to do both.  &quot;Robbing Peter to pay Paul&quot;  In this case, Paul gets paid. If you were to rob Peter to pay Paul, and get robbed yourself before you could get the money to Paul, that'd be closer. :)  &quot;Spreading yourself too thin&quot;  An actual English idiom, but missing the implied sense of failure.  &quot;Too many irons in the fire&quot;  &quot;A lot of irons in the fire&quot; can be viewed positively, so this is missing the sense of a strategic misstep.  &quot;Between a rock and a hard place&quot;  The sense is of needing to act but having no good alternative.  &quot;Falling between two stools&quot;  My favorite answer so far because it does appear to be an actual English idiom (not a proverb). In that sense, it's great, but some of the usages are closer to a failure of  than a failure of effort. And falling between two stools implies that the attempted action was simply sitting down.  &quot;Chasing two rabbits and catching none.&quot;  This is the exact sense I was looking for, but it appears to be a cross-cultural proverb rather than idiomatic English like &quot;putting all your eggs in one basket&quot;. I'll be accepting it, and using it in my work! But if there are other ideas, please let me know. Count and use the number of items in advance For each of the following, give an example of a sequence of functions $f_n$ that converges to f  A. uniformly but not in the mean square sense.  B. in the mean square sense but pointwise nowhere.  I know that for part A the domain of the function cannot be bounded but other then that I'm not sure how to go about the problem My laptop has 500gb hard disk in which for 250gb I installed Windows xp on C drive(primary partition). I want to install Ubuntu 12.04 in the remaing hard drive with dual boot option. When I am going to install Ubuntu it is showing something like  /boot /boot/   Can anybody help me in this regard that where and how to install Ubuntu? Difficult Polynomial Question Does anyone know of any good tools (I'm looking for IDEs) to write assembly on the Mac. Xcode is a little cumbersome to me.  Also, on the Intel Macs, can I use generic x86 asm?  Or is there a modified instruction set? Any information about post Intel.  Also: I know that on windows, asm can run in an emulated environment created by the OS to let the code think it's running on its own dedicated machine. Does OS X provide the same thing? I am relatively new to game development, and am working on a simple 2D platformer. I have created a tilemap and painted some tiles for the character to walk on.. but he is getting stuck. Yes, I know this is a common question and I did find some answers (including this one: ), but none seem relevant for me. The thing is my tiles are not flat.. they have pointy edges due to grass.. see the image below:  As you can see, the edge is not flat. I have overcome the problem of getting stuck by changing the &quot;Edge Radius&quot; to what you see in the above screenshot and that works, but the character now looks like he is floating slightly above the ground. Is there any way I can just tell Unity to ignore the jagged grass and make the collider flat and move the edge of it down a bit? That way it would fix the issue and also have the added bonus of looking like some of the grass is behind him and some in front.. Since  from other SE sites and is not thought to point out a lack of quality or helpfulness, but only to express agreement or disagreement, I'm wondering why downvoted answers here on meta are shown semi-transparent.  Shouldn't they be non-transparent then (like upvoted answers)?  Or am I missing something? Is it a good idea to take a break from studying a mathematics PhD and revisit academia at a later stage? I am currently using Ubuntu 10.04. I know there is a 10.10 release, but can I upgrade directly to 11.04? Could you walk me through the steps please? How can I cure lycanthropy? I really want to get rid of it. I've been through the whole companion’s quest line and cured Kodlak's. I killed all 5 witches and have 4 of the heads left in my inventory.  I've been back to that same flame and tried to use it with the head, but nothing going; activating it does nothing. I've heard this is how you cure it; however I have not heard a first-hand account of anyone actually curing it.  If you have, can you explain what you do? Do you go to the same tomb where you fought Kodlak's beast form? Do you do something special with the witch head in your inventory, or just have it in there and activate the harbinger flame or whatever? Sum over all non-evil numbers Understanding Group Permissions How to understand linux versioning I need to understand the Linux versioning system and distribution concepts. what are public, stable or final terms for versions? Enqueue Stylesheets After Theme's "rtl.css" I am currently developing a theme with internationalization support, and would like to load stylesheets after my theme's rtl.css (an alternative style.css loaded for languages with a right-to-left reading order).  I am familiar with enqueueing my stylesheets and controlling their load order with dependencies using the wp_register_style() and wp_enqueue_style() functions, however rtl.css is loaded automatically by WordPress whenever the locale's language direction is rtl, and there doesn't seem to be a way to specify the stylesheet as a dependency.  I know I can conditionally enqueue stylesheets using the is_rtl() function, however  these stylesheets' &lt;link&gt; elements are still printed out before WordPress automatically prints rtl.css's. I could also simply manually insert &lt;link&gt;s to the stylesheets that I wish to depend on rtl.css right after the call to wp_head() in my theme's header.php file, but I believe it's bad practice to do so, and I would like my theme to be commercial quality.  How can I load stylesheets after WordPress loads rtl.css? How to find all files with the same extension within a directory I want to search for all .conf files in /etc/. I tried grep -r *.conf /etc, but the result isn't right. What am I doing wrong? Isomorphisms preserving integral domains and fields Let $R \simeq S$ be isomorphic commutative rings with unity. Prove the following:  a). If $R$ is an integral domain then $S$ is an integral domain.  For this, I said that If I let $f: R \to S$ be an isomorphism and $(R, + , \circ), (S, \oplus, \ast)$, then let $x, y\in R$,  such that $x \circ y = 0_R$, because $f$ is an isomorphism, $f(x \circ y) = f(x) \ast f(y) = f(0_R)$. If I let $R$ be an integral domain then, as per the definition $R$ is commutative, has unity, and no zero divisors.   So $f(x \circ y) = f(x) \ast f(y) = f(0_R)$ where we have either $f(x \circ y) = f(0_R) \ast f(y) = f(0_R)$ or $f(x \circ y) = f(x) \ast f(0_R) = f(0_R)$.   Since $f$ is an isomomorphism, let $s = f(x), t = f(y)| s,t \in S$. Then $s \ast t = f(0_R)$. By definition, $S$ also has unity so $0_S$ exists. If we map $0_R \to 0_S$. Then either $s = 0_S$ or $t = 0_S$.   So then, since $S$ has unity, is commutative, and has a no zero divisors as we showed above, it is also an Integral domain.  I'm not sure I have this correctly.  b). If $R$ is a field then $S$ is a field. I don't really understand how to do this one. Since $S$ is an integral domain, it has a $0_S$. So I need to show that $S$ distributes $\ast$ over $\oplus$.  Any help with these is appreciated GitHub pages are not updating