According to the Monty Hall Problem, I select a door, say door number $1$. Monty then opens $3$ of the remaining $6$ doors that do not contain the prize. The question is should I switch.  Note that all the doors are said to have equal chance of containing the prize.  My attempt: $$P(1) = \frac{1}{7}$$  Once Monty opens three doors, we know that none of them contain the prize, so, we update our beliefs $$P(i|j, k, m) = \frac{1}{4}$$  Thus any of the closed doors has probability $\frac{1}{4}$ of containing the prize, so switching is pointless.  What am I doing wrong here?
I just learned about the Monty Hall problem and found it quite amazing. So I thought about extending the problem a bit to understand more about it. In this modification of the Monty Hall Problem, instead of three doors, we have four (or maybe $n$) doors, one with a car and the other three (or $n-1$) with a goat each (I want the car).  We need to choose any one of the doors. After we have chosen the door, Monty deliberately reveals one of the doors that has a goat and asks us if we wish to change our choice.  So should we switch the door we have chosen, or does it not matter if we switch or stay with our choice?  It would be even better if we knew the probability of winning upon switching given that Monty opens $k$ doors.
I have been running  over some C# code, and it keeps reporting that my using directives should be inside the namespace.  Is there a technical reason for putting the using directives inside instead of outside the namespace? How do you decline nouns borrowed from languages with several categories for declining nouns (or none at all)? what do it mean by "A real nxn matrix always has a real eigenvalue when n is odd?" Shouldnt it be that regardless of odd or even there will always have a real root?  hope to hear from you guys soon:) Rounding to nearest 100 First number needs to be rounded to nearest second number. There are many ways of doing this, but whats the best and shortest algorithm? Anyone up for a challenge :-)   1244->1200  1254->1300 123->100 178->200 1576->1600 1449->1400 123456->123500 654321->654300 23->00 83->100 I want to find a set of integer solutions of Diophantine equation: $ax + by = c$, and apparently $\gcd(a,b)|c$. Then by what formula can I use to find $x$ and $y$ ?   I tried to play around with it: $x = (c - by)/a$, hence $a|(c - by)$.     $a$, $c$ and $b$ are known. So to obtain integer solution for $a$, then $c - by = ak$, and I lost from here, because $y = (c - ak)/b$. I kept repeating this routine and could not find a way to get rid of it? Any hint?  Thanks, Chan Check to see if an email is already in the database using prepared statements simple process builder failing with error "failed to access the value for variable because it hasn't been set or assigned" Note: This error might look like a familiar error but the   resolution mentioned in the  is not working in the below case and I am not sure why, hence posting this question.   Problem description:   I have a process builder on case object set to fire for every time new record is created. Criteria is set to 'Formula evaluates to True' with below formula: AND(NOT(ISBLANK([Case].AccountId)),ISPICKVAL([Case].Account.Active__c,'Yes')) With immediate action set to update custom field on the Case object. Custom field Active__c on the Account object is type picklist with two possible values 'yes' and 'no'.   Screenshots of the process builder:        Creating a case as shown in the below screenshot with very minimal details and especially not populating account details:    Throws below error:     The flow failed to access the value for   myVariable_current.Account.Active__c because it hasn't been set or   assigned.   Relevant data from log file:     22:14:31.0 (12479016)|WF_FLOW_ACTION_BEGIN|09L370000000FEJ 22:14:31.13   (13607478)|FLOW_CREATE_INTERVIEW_BEGIN|00D37000000H8hr|300370000008ZTl|301370000004weE   22:14:31.13   (15394571)|FLOW_CREATE_INTERVIEW_END|5525dfa7819c33f438ce3cef9b6c15c668d8ff2-3d11|Test   22:14:31.15 (15820974)|FLOW_START_INTERVIEWS_BEGIN|1 22:14:31.15   (16674702)|FLOW_START_INTERVIEW_BEGIN|5525dfa7819c33f438ce3cef9b6c15c668d8ff2-3d11|Test   22:14:31.15 (35470120)|FLOW_ELEMENT_ERROR|The flow failed to access   the value for myVariable_current.Account.Active__c because it hasn't   been set or assigned.|| 22:14:31.15   (35479812)|FLOW_START_INTERVIEW_END|5525dfa7819c33f438ce3cef9b6c15c668d8ff2-3d11|Test 22:14:31.15 (35517783)|FLOW_START_INTERVIEWS_END|Interview error.   Aborting all.|5525dfa7819c33f438ce3cef9b6c15c668d8ff2-3d11|Test   22:14:31.15 (35528335)|FLOW_START_INTERVIEWS_END|1 22:14:31.0   (35588898)|WF_FLOW_ACTION_ERROR|09L370000000FEJ|300370000008ZTl|Error   executing flow: test, FlowDefId: 300370000008ZTl, FlowVersionId:   301370000004weE 22:14:31.0   (35612585)|WF_FLOW_ACTION_ERROR_DETAIL|An unhandled fault has   occurred in this flowAn unhandled fault has occurred while   processing the flow.  Please contact your system administrator for   more information. 22:14:31.0   (35683203)|WF_FLOW_ACTION_END|09L370000000FEJ   URL to the complete debug log :  (Note: You can see from the log that there are no other workflow rules or triggers on the case object).  My analysis: When the first condition inside the AND expression is evaluating as false, why is it trying to evaluating the second condition to check the custom field on the Account object? It shouldn't right?  Any help?  EDIT: I am looking to solve this using option 'Formula Evaluates to True' only because I have other complex criteria like checking the day(Mon vs Tue and etc) of the case creation. Pandemic, Global Epidemic, Epidemic, Endemic I really want to hear from the experts the definitions of all 4 terms especially whether global epidemic is equivalent to pandemic. Or should this question be directed to the epidemiologist?   Pandemic Global Epidemic Epidemic Endemic   I have Googled the terms and I understand the definition of 1), 3) and 4). In short the definition is based on geographical location and scale of outbreak, Pandemic is an outbreak of disease on a global scale (e.g. HIV). Epidemic is an outbreak of disease on a localised area. Endemic is a disease in a localised area. However, a definition for Global Epidemic is not available online.  Recently, WHO mentioned that "“It is important to put this on the table: this virus(Covid19) may become just another endemic virus in our communities, and this virus may never go away,” WHO emergencies expert Mike Ryan told an online briefing." Isn't covid19 considered a pandemic since it is on a global scale and is spreading rapidly?  Another term that I come across often is Global Epidemic. For example in the WHO website, HIV is listed as Global Epidemic. Does that mean Pandemic and Global Epidemic are the same? Multi armed bandit for general reward distribution I'm working on a multi-armed bandit problem where we do not have any information about the reward distribution.   I have found many papers which guarantee regret bounds for a distribution with known bound, and for general distributions with support in [0,1].   I would like to find out if there is a way to perform well in an environment where the reward distribution does not have any guarantees about its support.  I'm trying to compute a nonparametric tolerance limit and using that number to scale the reward distribution so I can use the algorithm 2 specified on this paper (). Does anyone think this approach will work?  If not, can anyone point me to the right spot?  Thanks a bunch! I read a comment under :     There are plenty of events that can occur that have zero probability.   This reminds me that I have seen similar saying before elsewhere, and have never been able to make sense out of it. So I was wondering    if zero probability and impossibility mean the same? if an event with zero probability doesn't mean that the event is impossible to occur, how probability theory represents/describes impossibility?   Thanks and regards! A financial planner treated us in a dismissive fashion and I want to say that he "gave us the back of his hand" but that phrase doesn't seem to have the meaning of dismissive. Does it or is there a similar idiom? Was Yoda fully sane on Dagobah? Our (and Luke's) original impression of Yoda is by no means flattering. He looks like a crazy hungry green thing that unfortunately has the ability to speak. Yoda digs through Luke's stuff, eats Luke's food, and, obsessed with that awesome little flashlight, ends up stealing it. (He even goes so far as to fight with Artoo over it.)  So was Yoda slowly losing it during all those years as a hermit?  Perhaps going from fighting battles and conversing with others on a daily basis to living in total isolation with no one to speak with would play a part in that? Or could Yoda have been faking his apparent insanity for some reason? (If so, what is mentioned reason?) I am wondering whether there is any difference between a gerund acting as subject and an infinitive acting as a subject. I've been wondering, what is the difference between seek and search? When should one be preferred over the other? One Object won't Show up in Final Render even though it shows up in the Preview Render I have a model of a building with a sidewalk around it.  Both show up when I switch to rendering mode in both Blender Render and Cycles Render mode.  But:  when I hit F12 for a final proper render, the building shows up -- but the sidewalk doesn't.    I've checked the normals and I thought the normals seemed pointed in the right direction.  I've set the Clipping on the Camera to a high number.  I removed all the materials from the sidewalk and added a new material-- the problem persists.  I've exported the blend as an FBX file and the Sidewalk shows up fine in Unity.  Just in final renders, it doesn't show up.    Here is a blend file: .  I tried to destroy everything unrelated to the issue and label things in a clear way.    Thanks. How can I tell which version of Windows 8 I am running? Standard, Pro, Enterprise, or RT? I have searched everywhere but cannot find how to tell which version of Windows 8 I am running.  I have the system properties on the screen but it just says "Windows 8," nothing else.  Is this the standard edition?  EDIT 04142015:  My new favorite way to do this is to go to the commnand prompt and issue (same with Windows 7):    wmic os get caption  Response:  Microsoft Windows 8.1 Pro Is there a pronoun I can use as a gender-neutral pronoun when referring back to a singular noun phrase?  Each student should save his questions until the end. Each student should save her questions until the end. This is not a duplicate of this .  The linked question says that it suffices to show that if $(x_n)\to x$ then $(\frac{x_1+\cdots+x_n}{n})\to x$ to prove my question, but how so? I tried using the same strategy as how one proves that if $(x_n)\to x$ then $(\frac{x_1+\cdots+x_n}{n})\to x$, by "splitting" the product in th $N$th term:  $$\sqrt[n]{x_1x_2\cdots x_n}=\sqrt[n]{x_1x_2\cdots x_Nx_{N+1}\cdots x_n}=\sqrt[n]{x_1x_2\cdots x_N} \sqrt[n]{x_{N+1}\cdots x_n}$$  but it seems I can't use for now the definition of convergence of $(x_n)$ because of the $n$th root. I also tried to use a result: if $(x_n)\to x$ then $(\frac{x_n}{n})\to 1$ but don't know if this is true. Sadly I've had no real progress. Any help will be greatly appreciated, thanks in advance! Moving app to production mode in Symfony 2 Draw a vertical line over the entries of a column in an array I'd like to draw vertical/horizontal lines over the entries of a column/row in an array. I find the method to draw horizontal lines at . But when I used the same way to draw the vertical lines. It didn't look well. My codes are:  \usepackage{tikz} \usetikzlibrary{calc} \newcommand{\tikzmark}[1]{\tikz[overlay,remember picture] \node (#1) {};} \newcommand{\DrawLine}[3][]{% \begin{tikzpicture}[overlay,remember picture]     \draw [#1] ($(#2)+(0,0.6ex)$) -- ($(#3)+(0,0.6ex)$); \end{tikzpicture}% }%  \begin{displaymath} \left[ \begin{array}{cccc} \tikzmark{11}{15} &amp; 0 &amp; \tikzmark{13}{0} &amp;0\tikzmark{14} \\ 0 &amp; 50 &amp; 20 &amp; 25 \\ 35 &amp; 5 &amp; 0 &amp; 10\\ \tikzmark{41}{0} &amp; 65 &amp; \tikzmark{43}{50} &amp; 65 \end{array} \right]. \DrawLine[black,thick]{11}{14} \DrawLine[black,thick]{11}{41} \DrawLine[black,thick]{13}{43} \end{displaymath}   The result looks like     But the result I want is     Does anyone know how to fix this? Thank you.