I just finished writing for one of them but I still have two more to write. Though my interactions with all three of them have been on different occasions, there are still limited things I can write about myself without overdoing things. I am just not sure how should I approach writing the rest two? Should I just repeat everything I wrote in the first one? I am quite sure they will add/remove a couple of lines only. So if I just copy the contents, they will look all the same. If I don't then I fear I will miss important points about myself.
If a student needs a reference letter for graduate admissions or that sort of thing, some profs will ask the student to write a reference letter for themself before sending it off to the prof for minor edits and finalization. This seems to be a somewhat common practice given that some graduate schools ask for several letters of recommendation even when it is not reasonable for the student to have developed deep connections with that many professors, and that most professors are just too busy to write quality letters for all the students that ask them to.  Is it acceptable to write most of the reference letter and have the prof make minor edits? Do academic institutions frown upon this practice? Would it be considered an academic offense if a student wrote a reference letter for themselves and had a prof sign it?
Simulating draws from a Uniform Distribution using draws from a Normal Distribution I recently purchased a  in which one of the probability questions was as follows:     Given draws from a normal distribution with known parameters, how can you simulate draws from a uniform distribution?   My original thought process was that, for a discrete random variable, we could break the normal distribution into K unique subsections where each subsection has an equal area under the normal curve. Then we could determine which of K values the variable takes by recognizing which area of the normal curve the variable ends up falling into.   But this would only work for discrete random variables. I did some research into how we might do the same for continuous random variables, but unfortunately I could only find techniques like inverse transform sampling that would use as input a uniform random variable, and could output random variables from some other distribution. I was thinking that perhaps we could do this process in reverse to get uniform random variables?  I also thought about possibly using the Normal random variables as inputs into a linear congruential generator, but I'm not sure if this would work.  Any thoughts on how I might approach this question? How to add System.Windows.Interactivity to project? How do I get Skyrim to recognize I don't have a follower anymore? How to find a 4D vector perpendicular to 3 other 4D vectors? In 3 dimensions it is possible to find a vector c (one of infinitely many) perpendicular to two vectors a and b using the cross product. Is there any way of extending this to 4 dimensions, i.e. given three vectors a, b, and c finding a vector d perpendicular to all of them?  I realize that this can be done by solving the equation system:  dot(a, d) = 0 dot(b, d) = 0 dot(c, d) = 0   and imposing an additional constraint, for instance setting the length of d to or one of its components to 1, but is there a way of doing this that does not involve solving an equation system? "Unfortunately, ... has stopped" when Downloading file in Android When I define amsthm theorem environments with shared counters, autoref messes up the names of the references. For example, in the output below, we should have "Definition 2" instead of "Theorem 2".  \documentclass{article}  \usepackage{amsthm} \usepackage{hyperref}  \theoremstyle{theorem} \newtheorem{theorem}{Theorem} \theoremstyle{definition} \newtheorem{definition}[theorem]{Definition}  \begin{document}  \begin{theorem} \label{wonderful-theorem} This is a wonderful theorem. \end{theorem}  \begin{definition} \label{awesome-definition} This is an awesome definition. \end{definition}  Look at the wonderful \autoref{wonderful-theorem} and the awesome \autoref{awesome-definition}.  \end{document} Why is it called Area 51? According to : "We like the little aliens."  This seems well targeted to appeal to the Stack Overflow / Server Fault / Super User audience, but way off the mark if the goal is to "make the Internet a better place to get expert answers to your questions."    There are experts who aren't interested in or focused on technology oriented topics.  Little aliens are unlikely to be something that someone interested in organizing a site on gardening would gravitate too.  No, I'm not suggesting that no one interested in gardening would be bother to look at a site with little aliens, but won't it be likely that the sort of mass appeal to to a very broad cross section of the internet will be lacking? How to increase the width and height of the Rich Text area field in Visual force Page? Can't install aircrack-ng Whenever I attempt to install aircrack-ng in terminal I get the following error:  Package aircrack-ng is not available, but is referred to by another package. This may mean that the package is missing, has been obsoleted, or is only available from another source However the following packages replace it:   iw  E: Package 'aircrack-ng' has no installation candidate"   I'm new to Ubuntu and so have no idea what to do. How much marmelade can I bring into the US? I want to bring homemade berry marmelade in little glass jars with me to the US from Europe as gifts for friends. I have found the following site on importing foods into the US  and would assume that marmelade falls under the condiments category, which should be admissible. However, I am wondering however if there is any limit to how much one is allowed to bring. Will there be any issues if, say, I bring 3 kilograms (6 lbs 10 oz)?   Also on related note, would they be suspiscious when they see many glass jars in my bag? Do I risk getting my bag searched or getting asked what the jars are? Is there anything I can do to avoid any such trouble? Why does Javascript getYear() return 108? Why does this javascript return 108 instead of 2008? it gets the day and month correct but not the year?  myDate = new Date(); year = myDate.getYear();   year = 108? I am studying for an exam and I am having trouble with this practice question:  In this question, we consider finite bit strings that do not contain $00$. Examples of such bitstrings are $0101010101$ and $11110111$. For any integer $n\geq 2$, let $B_n$ be the number of bitstrings of length $n$ that do not contain $00$.   Determine $B_2$ and $B_3$. Prove that $B_n = B_{n-1} + B_{n-2}$ for each $n\geq 4$. For each $n\geq 2$, express $B_n$ in terms of a Fibonacci number.   Any help is greatly appreciated Tail sum for expectation In , the tail sum formula for expectation is introduced for a nonnegative (0,1,...) discrete random variable $X$:  $$E(X) = \sum_{i=0}^\infty P(X &gt; i).$$   I wonder if there is a similar formula for nonnegative continuous random variable $X$:  $$E(X) = \int_0^\infty P(X &gt; x) dx?$$  If no, are there some conditions for it to hold? And how can it be proved?  Here is my thought:  If the cdf $F$ of $X$ is bijective, then $X=F^{-1}(U)$ for some random variable $U$ uniformly distributed over $[0,1)$. So $$E(X) =     \int_0^1 F^{-1}(u) du.$$  To prove the tail sum formula, it suffices to prove $$\int_0^1     F^{-1}(u) du = \int_0^\infty P(X &gt; x) dx.$$ But I am stuck here.   What's more, is the condition that the cdf $F$ of $X$ is bijective really necessary for tail sum formula to hold? Can tail sum formula be generalized to a random variable that is not necessarily nonnegative?   Thanks! Apparently this is a  and should hopefully be fixed in an upcoming update.    I have installed SQL Server Management Studio v17.9 on a clean Windows 10 installation.  This associated all .sql files with SSMS.  I want to associate .sql files with a plain text editor (eg: Sublime) but I am unable to change the default application.  I have tried:   Right click .sql file -> Open With -> Sublime + "Always use this program". Settings -> Default Applications by File Type -> Find .sql -> Change to Sublime Right click .sql file -> Properties -> "Change" button -> Sublime. Using ftype via elevated command prompt as seen    In all 3 cases, my selection is not reflected in any way, anywhere.  The icon remains SSMS, and the file opens with SSMS.  Is there some kind of "File Association retention" setting within SSMS I am unaware of?  Edit: I can change the default application for non-SSMS-associated extensions without issue.  Edit: after deleting registry key HKCU\Software\Microsoft\Windows\CurrentVersion\Explorer\FileExts\.sql, .sql files show a VSCode icon:    If I then double-click New Users.sql, it opens with SSMS and a refresh of regedit shows the .sql entry recreated with ssms.exe associated (the icon remains VSCode):    If I then right-click -> open with -> Choose Another App -> Select Sublime and hit "Always use this to open .sql files", it opens with Sublime and a refresh of regedit shows a new "b" entry created for Sublime.  The icon remains VSCode, and double-clicking opens it in SSMS:    If I then delete the a entry for ssms.exe and rename b -> a such that only sublime exists, then double-click the .sql file, it opens with SSMS and generates a new b entry for itself: Direction of $d\mathbf{l}$ A solid sphere has charge $q$ and radius $R$. Find the potential at a point a distance $r$ from the center of the sphere where $r&gt;R$, using infinity as the reference point.  My attempt:  From Gauss' theorem we may deduce that $\displaystyle\mathbf{E}=\frac{1}{4\pi\epsilon_0}\frac{q}{r'^2}\hat{\mathbf{r}}$ where $r'$ is the distance of an arbitrary point from the center of the sphere provided $r'&gt;R$.  $V=-\int_\infty^\mathbf{r}\mathbf{E}\cdot d\mathbf{l}$  My question: What is $d\mathbf{l}$? Since we are traversing in the direction opposite to $\hat{\mathbf{r}}$, I think it should be $-dr'\hat{\mathbf{r}}$. But when I use it to find $V$, I get a sign error. Please help! Do I need to have antivirus software installed? How to Customize the Email template on chatter posts Is the set of all finite sequences of letters of Latin alphabet countable/uncountable? How to prove either? Today in Coding/Cryptography class, we were talking about basic definitions, and the professor mentioned that for a set $A=\left \{ \left. a, b, \dots, z \right \} \right.$ (the alphabet) we can define a set $A^{*}=\left \{ \left. a, ksdjf, blocks, coffee, maskdj, \dots, asdlkajsdksjfs \right \} \right.$ (words) as a set that consists of all finite sequences of the elements/letters from our $A$/alphabet. My question is, is this set $A^{*}$ countably or uncountably infinite? Does it matter how many letters there are in your alphabet? If it was, say, $A=\left \{ \left. a \right \} \right.$, then the words in $A^{*}$ would be of form $a, aa, aaa, \dots$ which, I think, would allow a bijection $\mathbb{N} \to A^{*}$ where an integer would signify the number of a's in a word. Can something analogous be done with an alphabet that consists of 26 letters (Latin alphabet), or can countability/uncountability be proved otherwise? And as mentioned before, I am wondering if the number of elements in the alphabet matters, or if all it does is change the formula for a bijection.   P.S. Now that I think of it, maybe we could biject from $\underset{n}{\underbrace{\mathbb{N}\times\mathbb{N}\times\mathbb{N}\times\dots\times\mathbb{N}}}$ to some set of words $A^{*}$ whose alphabet $A$ has $n$ elements? Thanks! I followed the instructions and got success response but I didn't receive email.  Then I used the id to get Email Status and got 404 error.  Here is my json :  POST :   {     "To": {         "Address": "example@gmail.com",         "SubscriberKey": "example@gmail.com.tw"     },     "Options": {         "RequestType": "ASYNC"     } }   GET : {id}  Please let me know how I can resolve the issue. For the finite-dimensional case, we have a canonical isomorphism between $\mathbf{V}$, a vector space with the usual addition and scalar multiplication, and $(\mathbf{V}^*)^*$, the "dual of the dual of $\mathbf{V}$." This canonical isomorphism means that the isomorphism is always the same, independent of additional choices.   We can define a map $I : \mathbf{V} \to (\mathbf{V}^*)^*$ by $$x \mapsto I(x) \in (\mathbf{V}^*)^* \ \text{ where } \ I(x)(f) = f(x) \ \text{for any } \  f \in \mathbf{V}^*$$  My Question: what can go wrong in the infinite-dimensional case? The notes I am studying remark that if $\mathbf{V}$ is finite-dimensional, then $I$ is an isomorphism, but in the infinite-dimensional case we can go wrong? How?