Simulate a fair coin toss with a biased die?
Can a coin with an unknown bias be treated as fair?
Does there exist a holomorphic function with the following property? Expected value in an urn problem In an urn there are $n$ red balls and $m$ blue balls. I extract them without replacement. Let $X$=time of first blue. What is $E(X)$?  I found PMF of $X$ and it is, if $k &gt; n+1$  $$P(X=k) =\frac{n(n-1) \dots (n-k+1)m}{(m+n)(m+n-1) \dots (n+m-k+1)}$$  How could I evaluate $E(X)$?  Edit: I'm looking for an explicit form of $E(X)$ Java equivalent of unsigned long long? In C++, I enjoyed having access to a 64 bit unsigned integer, via unsigned long long int, or via uint64_t. Now, in Java longs are 64 bits, I know. However, they are signed.  Is there an unsigned long (long) available as a Java primitive? How do I use it? Frequency of the sound when blowing in a bottle If I have the following state:  $$ \left| \varphi \right&gt;=\frac{1}{\sqrt{2}}\left(\left(\frac{1+i}{\sqrt{2}} \right)\left| 0 \right&gt; + \left| 1\right&gt;\right) $$  How can I find the $\theta$ and $\phi$ values of this qubit on the Bloch sphere? I think the title says all I want: I want to add context menu items for a specific file type like the yellow marked ones in the screenshot. Which registry changes do I have to make? In my case I want to assign ir.exe to .rb files. I want to run DFS replication between a couple of servers. It's my understanding that the servers need to be part of a domain for this. Being able to give people a username and password that works on all servers would be useful too, so I can lock up the admin password.  All machines will be running Windows 2008R2 and they will all be running Windows Firewall, so I need to be able to allow the other machines to connect to this server, but lock out everyone else.   So my question is: what ports do I need to allow the machines to connect to the Domain Controller over? Rounded corners in TikZ trees. \includegraphics PDF, color problem I'm using pdflatex, and use \includegraphics to include content of figures from PDF. PDF are exported from InkScape.  \begin{figure} [!h]     \centering     \includegraphics[height=3cm]{fig/SUSAN.pdf} \end{figure}   Included PDF or source SVG has same colors. Green has always RGB value (0, 255, 0). Problem occurs when I include this files from LaTeX. In output PDF on some pages colorspace is darker. Even same image on other page has different colourity.  My PDF  . As you can see on page 7 (11 in PDF) USAN areas are bright green, but then on page 5 (9 in PDF) are green points on corners more darker. I have created my StackOverflow Careers panel, and when I click 'add a stack overflow account with over 200 reputation' the site decides that I have no StackOverflow account at all, although my current one has over 300. I log in to both with the same StackExchange Account with the same email etc so I'm curious as to why this is happening. "Available jobs to/for them" First of all, English is not my first language. I have a question, maybe a basic one, about this phrase:     The situation highlights the mismatch between some areas of training and available jobs to/for them.   Should it be "available jobs to them" or "available jobs for them"?  Sorry if the question is really basic. How can I send an email by Java application using GMail, Yahoo, or Hotmail? Is it possible to send an email from my Java application using a GMail account?  I have configured my company mail server with Java app to send email, but that's not going to cut it when I distribute the application. Answers with any of using Hotmail, Yahoo or GMail are acceptable. Unable to disable assignment rules I have a condition where I need to disable standard Lead Assignment Rules if certain criteria are met.   if(emailWithAccIdMap.containsKey(ledRec.Email) &amp;&amp; emailWithAccIdMap.get(ledRec.Email) != null &amp;&amp; !openOppMap.isEmpty() &amp;&amp; openOppMap.get(emailWithAccIdMap.get(ledRec.Email)) != null &amp;&amp; openOppMap.get(emailWithAccIdMap.get(ledRec.Email)).Owner.isActive ==true){                     ledRec.Status = 'Duplicate';                     System.debug('Changing the Status');                     //then assign the original lead owner to new lead owner                     ledRec.OwnerId = openOppMap.get(emailWithAccIdMap.get(ledRec.Email)).OwnerId;                     ledRec.Account_Name__c = openOppMap.get(emailWithAccIdMap.get(ledRec.Email)).AccountId;                     ledRec.Field_for_Lead_Workflow__c = true;                     Database.DMLOptions dmo = new Database.DMLOptions();                     dmo.assignmentRuleHeader.useDefaultRule = false;                     ledRec.setOptions(dmo);                     //since owner is assigned, it shouledRec not pass through round robin                     ledRec.checkAssignment__c = false;  }   This is my code snippet which is running on before insert. The control is entering the IF condition as the debug statement is getting printed. Yet, the owner assigned through this snippet is being overridden by the assignment rules.  I also tried executing this in after insert trigger context but it did not work. Can somebody tell me what I'm doing wrong? Add max value to a new column in R Biber 2.14 - Puzzling repeated error : "Invalid format '2020-01-01' of date field 'date' - ignoring" Peppers evolved chemicals like capsaicin to discourage animals from eating them, and that chemical itself can cause internal damage if consumed in large quantities, though this is usually only a concern for the hottest of peppers (which people do eat).   Still, why is it that humans seem to be the only animal that often "like" spicy food? Why does my wildcard SSL certificate cause a domain mismatch error on a second level subdomain? Vector. Properties It is given in a question that $\vec x+\vec a=(\vec a\cdot \vec x)\vec b$ and it is stated that $\vec a$, $\vec b$ and $\vec x$ are vectors.  It is also stated that $\vec a\cdot \vec b\ne 1$.  The question asks to express $\vec x$ in term $\vec a$ and $\vec b$.  How do you this? What is a good method for short text clustering? I am working on a text clustering problem. The data contains several sentences. Is there a good algorithm which reaches high accuracy on short text?  Can you provide good references?   Algorithms such as KMeans, spectral clustering does not work well for this problem. Using v2.73, cycles and a very simple scene: an array of cubes, no big deal.   If I set the shader's material to transparent, the cubes in the foreground do become transparent but those far away in the back do not disappear completely and this strange dark things appear (visible in rendered mode and in final renders)    I've played with the clipping distance on the viewport and camera, but I can't figure out how to make those ghosts go away...