Yeah, like in the title, how do Regular Conditional Probabilities assign values to $P(A|B)$ when $P(B) = 0$? Because I am not trained in advanced probability, please explain it as simply as possible. It'll be great if you can demonstrate with an example. Let $X$ be a random variable between $[0, 1]$. What is the $P(X=\frac{2}{3}|X=\frac{2}{3})$?  Also, can it also assign values to $P(A|B)$ in finite spaces? For example, imagine you throw a die, and you observe that the die landed on an odd number at 12 noon. So letting $O$ be the event that the die landed odd, $P(O)$ changes from $\frac{1}{2}$ to $1$ after noon. Hence, after noon, letting $E$ be the event that the die landed even, $P(E)$ changes to $0$. But even after 12 noon, I still intuitively want to say that $P(E|E)$ is still $1$. It seems to me that for any non-empty set $A$ in the sigma-algebra, $P(A|A) = 1$. Can regular conditional probabilities assign $P(E|E)$  a value of $1$? Is it possible? Or do I need to give that intuition up? Thanks for your help.  Edit: I think my question is different from this:   Because I'm asking about finite spaces too. Also, I'm asking for a demonstration of how regular conditional probabilities assign value to $P(X=\frac{2}{3}|X=\frac{2}{3})$.  Edit 2: Let the sample space in the dice example be {1, 2, 3, 4, 5, 6}.  Edit 3: The sample space for the dice example is {1, 2, 3, 4, 5, 6}. The initial probability function before noon is $P$. After noon, the probability function becomes $P'$. So $P(O)$ = $P(E)$ = 0.5. But $P'(O) = 1$ and $P'(E) = 0$. Still, I want to say that $P'(E|E) = 1$.
Is there a way to resolve probability of an event, given another event that never happens? Mathematically speaking the problem is:  Given that $P(B) = 0$,  $$P(A|B)=\frac{P(A \cap B)}{P(B)} = \frac{0}{0}$$  Is this probability vacuously $0$ of $1$? Can we show that it's one or the other?
Elastic IP address on EC2 instance interface without 1:1 NAT I currently have a valid Schengen tourist visa that expires next year, issued by the French Consulate in Saudi Arabia.   I am going to a 60-day study abroad program in Italy and they require a student visa. I went to the Italian Consulate in Boston and they asked me to go to the French Consulate and cancel my visa. However, the French Consulate said that I needed to contact the French Embassy in Saudi to cancel the visa.   How can I cancel my tourist visa if I am currently in the United States? My Italian student visa application is due tomorrow morning. Teenage girl in life-sustaining valley on poisoned Earth visited by another survivor I'm trying to identify a book I read in school, though I can't recall at what grade level; let's say it had to have been published before I graduated high school in 2000. Despite being required reading, it didn't feel much like a classic.  The story took place on Earth, after some catastrophe had caused the air to become poisonous. However, one teenage girl was able to survive because her house was in a valley which was somehow protected from the poisonous winds and was able to sustain its own ecosystem. One day, a man wearing a protective full-body suit and gas mask appears in the valley, and both are rather surprised to find someone else alive. She feeds and shelters the man and shows him how she had come to survive in the valley. Rather abruptly…      the man attempts to rape her, but she overpowers him somehow. She steals his protective suit and starts to leave the valley. He tells her that he had seen birds in a certain direction away from the valley, indicating there might be life there as well, and she leaves.   I believe there was an author's note either at the beginning or end of the book stating that the author had actually died while writing the manuscript, and that their friends or family had finished the book by going off the author's original notes, which I suppose may explain the abruptness of the ending.  In case it wasn't clear from the above, I didn't really like the book. But I'm curious about it regardless. When a 'blur' event occurs, how can I find out which element focus went *to*? Suppose I attach an blur function to an HTML input box like this:  &lt;input id="myInput" onblur="function() { ... }"&gt;&lt;/input&gt;   Is there a way to get the ID of the element which caused the blur event to fire (the element which was clicked) inside the function? How?  For example, suppose I have a span like this:  &lt;span id="mySpan"&gt;Hello World&lt;/span&gt;   If I click the span right after the input element has focus, the input element will lose its focus. How does the function know that it was mySpan that was clicked?  PS: If the onclick event of the span would occur before the onblur event of the input element my problem would be solved, because I could set some status value indicating a specific element had been clicked.  PPS: The background of this problem is that I want to trigger an AJAX autocompleter control externally (from a clickable element) to show its suggestions, without the suggestions disappearing immediately because of the blur event on the input element. So I want to check in the blur function if one specific element has been clicked, and if so, ignore the blur event. Show $GCD(a_1, a_2, a_3, \ldots , a_n)$ is the least positive integer that can be expressed in the form $a_1x_1+a_2x_2+ \ldots +a_nx_n$ Given $a_1, a_2, a_3, \ldots , a_n$ not all zero, show $\gcd(a_1, a_2, a_3, \ldots , a_n)$ is the least positive integer that can be expressed in the form $a_1x_1+a_2x_2+ \ldots +a_nx_n$. Also deduce $a_1x_1+a_2x_2+ \ldots +a_nx_n = b$ has solutions $\iff \gcd(a_1, a_2, a_3, \ldots , a_n)|b$.   I know that $ax+by=n$ has integer solutions $\iff \gcd(a,b)|n$. I'll need to use induction to show $a_1x_1+a_2x_2+ \ldots +a_nx_n = \gcd(a_1, a_2, a_3, \ldots , a_n)$ has solutions, and then I will be able to say that as $\gcd(a_1, a_2, a_3, \ldots , a_n) | a_1x_1+a_2x_2+ \ldots +a_nx_n $ for any $x_1,x_2, x_3 \ldots x_n$ then $c \leq \gcd(a_1, a_2, a_3, \ldots , a_n)$ and $c \geq \gcd(a_1, a_2, a_3, \ldots , a_n)$, and thus $c=\gcd(a_1, a_2, a_3, \ldots , a_n)$. The muffins were rock hard, what did I do wrong? Here is the recipe I used, I did not mix it for long, as that make the muffins very hard.   The muffins were very hard, and had a bad after taste and smell. I missed adding some oil, but what else could be the reason ?   Red Millet Flour, 50 g Whole Wheat flour, 50 g Toasted Oat Bran, 40g Whole Green Mung Beans - Sprouted, 100 g Domino - Light Brown Sugar 50g Baking Soda, 2 tsp Salt, 1 Tablespoon Liquid Egg White, 4 eggs 100% Whey (Vanilla), 75g Chobani - Greek Yogurt - 0% Vanilla, 5.3 oz (small packet) Carrots - Raw, 1 cup, grated Bananas - Raw, 1 cup, mashed White, all-purpose, enriched, bleached, 40 g   Also I wanted to try yeast instead of baking soda, but due to eggs and other veggies I cannot let is rise overnight (any ideas ?). I was trying to make good protein muffins which are an ideal breakfast, grab one with a glass of milk and done!   They run approximately 160 calories per muffin 25g carbs, 1g fat, 12g protein. How should we handle a question which was deleted and reasked? A user has asked  which did not receive much attention, and thus the user deleted the post. After some time, the user asked the  (with just slight changes to the title and a tag change), so that it could receive a bit more attention. The strange thing is that the question was not downvoted or poorly written, and yet the user deleted the original post. Now, since the original question was deleted, I could not mark the new one as a duplicate (it threw an error). My question is, how do we handle such questions? Just let them be as such or let the user know about it or is there another way to handle such situations? How can I type "lambda-bar"? Center Gravity in Unity Does the mass of a battery change when charged/discharged? If so, how much? Is it possible to detect it, or is it beyond any measurement?  I'd say there are two possible scenarios (depending on the battery type) and both seem interesting:   The battery reacts chemically with its environment. The battery doesn't exchange any matter with its environment except electrons. I suppose there should be some difference at least due to the principle of energy-matter equivalence, but the difference is most likely immeasurable. Keytool Signing Problem: Keystore was tampered with, or password was incorrect What is the significance of allowing nilpotents in scheme theory? What purpose does downvoting questions serve? I want to  GRANT SELECT     ON ALL TABLES     TO foo;   But postgres tells me I have a syntax error at "TO". It expects a GRANT like:  GRANT SELECT     ON ALL TABLES     IN SCHEMA public     TO foo;   We have a handful of tables that have been sharded such that public, shard123, and shard124 all have a table my_table, and public.my_table is the parent of both shard123.my_table and shard124.my_table. I've GRANTed SELECT to foo for public schema, but foo doesn't have permission for any of the shard schemas.  I've also done:  ALTER DEFAULT PRIVILEGES     FOR ROLE dba     GRANT SELECT     ON TABLES     TO foo;   ...which should automatically grant for any new tables and schemas made from now on.  There are 1000 &lt; n &lt; 10000 shards/schemas, so GRANTing separately for each shard/schema is impractical.  How can I GRANT to a role for all existing tables across all existing schemas (all shards)?  Or even better, can I GRANT for all schemas LIKE 'shard%'? Symbol for “such that” (not in set) Prove that $\phi(n) \geq \sqrt{n}/2$ Evaluate the limit : $$\lim_{n \to \infty } {1 \over {\sqrt n }}\left( {1 + {1 \over {\sqrt 2 }} + {1 \over {\sqrt 3 }} + \cdots + {1 \over {\sqrt n }}} \right)$$  I can use the sandwich principle, certain convergence criteria, Cesaro mean theorem, limit arithmetic.. things around this area.  Any help would be greatly appreciated, thanks!  Sorry for not elaborating more at the beginning, rookie first-post mistake I suppose. :) I am giving a presentation and therefore I am using the  class. I have included some figures and it works, but there is no number after "Figure".  My code:  \documentclass{beamer}  \usepackage{graphicx} \usepackage[latin1]{inputenc} \usepackage[T1]{fontenc} \usepackage[english]{babel} \usepackage{listings} \usepackage{xcolor} \usepackage{eso-pic} \usepackage{mathrsfs} \usepackage{url} \usepackage{amssymb} \usepackage{amsmath} \usepackage{multirow} \usepackage{hyperref} \usepackage{booktabs} \usepackage{wallpaper} \usepackage{bbm} \usepackage{cooltooltips} \usepackage{eso-pic} \usepackage{everyshi} \usepackage{calc} \usepackage{graphicx} \usepackage{ifthen} \usepackage{graphicx} \usepackage{wrapfig} \usepackage{animate} \usepackage[singlespacing]{setspace} \usepackage[absolute,overlay]{textpos} \usepackage{enumerate} \usepackage{hyperref} \newenvironment{changemargin}[2]{%   \begin{list}{}{%     \setlength{\topsep}{0pt}%     \setlength{\leftmargin}{#1}%     \setlength{\rightmargin}{#2}%     \setlength{\listparindent}{\parindent}%     \setlength{\itemindent}{\parindent}%     \setlength{\parsep}{\parskip}%   }%   \item[]}{\end{list}}  \setbeamercolor{frametitle}{fg=red,bg=white}  \hypersetup{pdfpagemode=FullScreen} \renewcommand*{\UrlFont}{\normalfont}  \usetheme{Goettingen} \useinnertheme{circles} \beamertemplatenavigationsymbolsempty  \setbeamerfont{page number in head/foot}{size=\large} \setbeamertemplate{footline}[frame number]   %%% \begin{document}  \frame[plain]{ \titlepage }  \setbeamertemplate{background canvas}[default]  \frame{ \frametitle{}  \begin{figure} \begin{center} \includegraphics[scale=0.2]{varweakness} \caption{VaR as a quantile} \end{center} \end{figure}  }   \end{document}   Which gives the following frame with the figure:    (I am not sure what is causing the problem, therefore I did not delete any package.)  How can I get a number, e.g. Figure 1:? Cannot launch Minecraft: CertificateNotYetValidException What should I do when my Minecraft Launcher 1.3.11 wouldn't log me in? The console output is:                                              Sorry, but we couldn't connect to our servers. Please make sure that you are online and that Minecraft is not blocked. (CertificateNotYetValidException:NotBefore:Tue Apr 08 20:47:05 CST 2014) My fiancée and I are looking for a good Caribbean cruise in October and were wondering which islands are best to see and which Cruise line to take?  It seems like a lot of the cruises don't run in this month due to Hurricane season so I'm looking for other good options.  EDIT We'll be travelling in 2012.