EM algorithm for a binomial distribution
EM with Binomial
It is true that $P(X&gt;t+s|X&gt;t)=P(X&gt;s)$ for certain values $t$ and $s$.  However, how can I show that this still holds if:   $T$ is a continuous random variable. That is $P(X&gt;T+s|X&gt;T)=P(X&gt;s)$ Both $T$ and $S$ are continuous RVs: $P(X&gt;T+S|X&gt;T)=P(X&gt;S)$   All the random variables are independent. Is there a minimum damage rule? In D&amp;D3e, if you successfully hit a target you always did at least 1 point of damage (before applying Damage Resistance), even if you had a Strength penalty.  I can't find any mention of that rule in the 5e PHB.  Does the rule no longer apply, or did I just overlook it? The Next tag badge block overlaps the badge score block. Notification email from stackoverflow contains "<3" after zip code Let $\mathbb S = \varnothing$.      Then from the definition: $ \bigcap \mathbb S = \left\{{x: \forall X \in \mathbb S: x \in X}\right\}$      Consider any $x \in \mathbb U$.      Then as $\mathbb S = \varnothing$, it follows that: $\forall X \in \mathbb S: x \in X$ from the definition of vacuous truth.      It follows directly that: $\bigcap \mathbb S = \left\{{x: x \in \mathbb U}\right\}$      That is: $\bigcap \mathbb S = \mathbb U$. ()   Proofwiki uses the above "proof" to "prove" that intersection of the empty set is the whole universe.   My question is, is the use of vacuous truth really allowed in axiomatic set theory, like ZFC? I don't see how the use of vacuous truth is justified.   The next problem I can think of is that we cannot really "define" the elements of empty set (to my knowledge, there is no element in empty set) so how can we then prove as the above proof did? This seems to contradict the use of vacuous truth.  And of course, there is issue of using the whole universe as a set, and I don't think this is allowed.... (Maybe proof above is using a different axiomatic set theory, as I am using ZF-minded thoughts...) Our company would like to understand the effects:   If we have single table with Primary Key Identity column, int primary key IDENTITY(1,1),  and the Application is conducting multi-threading parallel processing, trying to conducts 1000s of simultaneous inserts on one table.   Would the identity primary key column fail, with a primary key violation in any way, for example: processors are trying to input the same identity number?  Or was SQL designed to be successful even in multithreading parallel insert?  Note: IDENTITY_INSERT is OFF Why is there a B in my flair? This was originally noticed and fixed back around the beginning of July. As of August 1, this problem seems to have returned. New bug report is here:   I just happened to notice that my SO flair has some sort of a B icon right before my username (instead of the expected site icon) Snapshot of the unknown icon:    My current (live) flair for monitoring:  It currently showing up like this for all users on all sites, but not on Combined or Meta flairs. For example Jon Skeet flair on programmers:    Live flair: Does anybody know how to add the shapefile name to a field in the file's attribute table?  I've found a description:     'You have to use inline variable in CalculateField like %Name% in   expresssion so that whatever the name of the file is, the string will   be inserted based on Name of the dbase file !'   I've tried to CalculateField tool with %Name%, but I got message:  Executing: CalculateField "2011-11-6 15_41_point" DBFName %Name% PYTHON # Start Time: Thu Dec 08 23:34:23 2011 WARNING 000405: No records within table Succeeded at Thu Dec 08 23:34:24 2011 (Elapsed Time: 1.00 seconds)   Where is my mistake? Motivated by :   Which finite groups are the group of units of some ring? Which finite groups are the group of units of some finite ring? Which finite abelian groups are the group of units of some commutative ring? Which finite abelian groups are the group of units of some finite commutative ring?   It  that even for fields this is not simple to answer.  I expect the general question (Which groups are the group of units of some ring?, with no finiteness hypotheses) is even harder. Why is "letter" not plural in "two letter words"? I have one feature-request with the objective of having duplicate questions with no answers:   To (try to) avoid people answering duplicate questions, add an alert that says the question has a probable duplicate if it has a close vote as Exact duplicate, asking the answerer to go to the original and answer there.   What do you think? My objective is letting the duplicate question exist for search purposes, but the answers centralized in the root question. What is the fastest way to convert float to int on x86 What is the fastest way you know to convert a floating-point number to an int on an x86 CPU.  Preferrably in C or assembly (that can be in-lined in C) for any combination of the following:   32/64/80-bit float -> 32/64-bit integer   I'm looking for some technique that is faster than to just let the compiler do it. In which cases is a word, or a group of words written in italics? Is italics used in specific contexts, or it is quite normal to write words in italics? Making adult decisions are/is really not fun.     What is the proper answer and why? My gut says "is" but I can't explain why. I want to package my project in a single executable JAR for distribution.  How can I make a Maven project package all dependency JARs into my output JAR? Completely synchronise multiple Macs Why are my quotation marks causing an “unexpected token” error with this command? I am really confused.  Which preposition is correct?     She is in/at the park.   They are in/at the park.   I am in/at the park.   Should I use in or at in these sentences? Divergent or not series? How tipe are this series?  $$\sum_{n=2}^\infty \frac 1 {n^2\ln n}$$ But $$\sum_{n=2}^\infty \frac 1 {n\ln n\ln(\ln n)}$$ I used Condensation Test, but I stack after that. Thanks! Tablet or Phone - Android