If $X_1,...,X_n$ are Bernoulli(p) iid then $X_1+...+X_n$ is Binomial(p,n)
Proof that a sum of Bernoulli rvs has Binomial distribution
The phrase for when: working in a group to divide responsibility and reduce malicious intent Why is my iPhone screen stuck on the 'connect to iTunes' screen? I need help with my iPhone. It's stuck on the 'connect to iTunes' screen.   iTunes does recognize the iPhone, but when I select 'restore', it goes through a few progress bars, then errors again. I've already tried to hard reset the phone, but that doesn't work either. ^@ spam in tty (but seems to be system-wide) I recently noticed some weird behavior on my GNU/Linux machine. I've been trying to narrow it down but I am unsure where to go next. My setup uses the following:   i3 gdm arch systemd grub2 pulseaudio 4.13.3-1-ARCH   Here is how it manifests iself:   when trying to resize panes in i3 (alt+right click and hold) the action will be randomly canceled (happens on key presses) alt+dragging windows meets a similar fate booting to tty periodically adds ^@s to the login prompt, I'd estimate them to be ~0.5s intervals in tty I can see those being passed to vim when I open the command bar (:) using a pager like less in tty mode and searching with / will result in  (?) being spammed htop's search (/) is instantly canceled by the periodic keypress  holding a key and trying to have it be repeated (such as holding space) will stop the other occurrences from happening (e.g. only one or two happen) any tooltip (such as chrome tooltips) get instantly closed because of key presses   Here is what I have tried:   tried switching DE temporarily (gnome, cinnamon, xfce) tried killing programs one by one until I was left with a tty session and essentially systemd services + pulseaudio tried booting on an arch livecd - problem does not manifest  overriding grub2 with init=/bin/bash drops me into a shell where the problem does not manifest I have tried pressing all keys to verify it wasn't a hardware problem, however previous steps point to it not being hardware I have made a diff of dmesg, from the init=/bin/bash and the regular boot - the main difference seems to be systemd being started in the regular boot Made a diff of lsmod from init=/bin/bash and regular boot, tried to rmmod modules that seemed related   My system is up to date, I'm not quite sure what other steps I can do to track this down. Any other debugging tips? Minimum of the Gamma Function $\Gamma (x)$ for $x>0$. How to find $x_{\min}$? Today a student asked me $\int \ln (\sin x) \, dx.$ Calculate the integral $$\int \ln (\sin x) \, dx.$$ Give an example of a sequence of continuous functions $f_n:\mathbb{R} \to \mathbb{R}$ such that the pointwise limit $f:\mathbb{R} \to \mathbb{R}$ exists but is discontinuous. My idea is $f_n(x)=\displaystyle\frac{x}{n}.$ Then the pointwise limit is $0$ but $f$ is discontinuous on $\mathbb{R}.$ Is that correct? I'm having a hard time understanding the definition of pointwise convergence. I have this definition: $\displaystyle\lim_{n\to \infty} f_n=f$ pointwise iff $\displaystyle\lim_{n\to \infty} f_n(x)=f(x)$ But then what is $f(x)$? Where does the $n$ go? In the example I gave, for instance, $\displaystyle\lim_{n\to \infty} f_n(x)=\displaystyle\lim_{n\to \infty} \frac{x}{n}=0.$ But does this equal $f(x)$? Is $f(x)$=0 a discontinuous limit? Delete all data for a kind in Google App Engine I would like to wipe out all data for a specific kind in Google App Engine. What is the best way to do this? I wrote a delete script (hack), but since there is so much data is timeout's out after a few hundred records. What does the AE/AF lock button do that half-pressing the shutter doesn't? The Sony A6000 has an AEL button, while Nikon SLRs have an AE/AF lock button. What do these do that half-pressing the shutter to lock focus and exposure, and then recomposing, doesn't? I'm used to the latter method, and never used a camera that has a dedicated button.  I read that you have to keep both the AE/AF lock button pressed and the shutter half-pressed while recomposing. Isn't this harder than just keeping the shutter button half-pressed?  I'm aware that you can customize the AE/AF lock button to lock only focus, or only exposure, or both. This leads to two follow-up questions:   Can't you customize the half-press shutter to lock only AE or only AF? If you don't care about this level of customization, does the AE / AF lock button do anything that half-pressing the shutter doesn't? Why is the voltage across a capacitor and the current across an inductor continuous? Why is the voltage across a capacitor (as a function of time) continuous? Why is the current across an inductor (as a function of time) continuous? I want to propose for a Persian version of Super User (I will explain why later) so I want to create a proposal in Area 51, but this means non-English question and answers, Is this OK? P.S: This may be a question for other non-English proposals too. Update: The main question is: How can non-English site proposals pass the Commitment phase? How can the English community support non-English proposals? You can find some information in  about the Stack Exchange 2.0 Site Creation Process (specially Commitment phase):  How does this thermometer work? Intuitively, if Jon Skeet says that he’ll participate in the Sock Puppet Stack Exchange, that commitment is a better sign that the site will succeed than if we get a commitment from a random Internet user who has never participated in Stack Overflow. Sure, they’re both wonderful people, I’m sure, but Jon Skeet has proven that he likes to participate in Stack Overflow so it’s a good bet that he’ll participate in SockExchange, too. .... we’re going to require a selection of existing users with certain badges and reputation that proves that they’ll participate. For instance (and I’m making these numbers up), we might require that a site get at least 100 commitments from people with the Teacher badge, at least 20 from people with the Enthusiast badge, and at least 50 from people with a reputation of 1000 or more on some of our sites. Security Review - CRUD/FLS Checks for every SOQL Query I know this sounds like a standard question, so please bear with me.  Recently our Security Reviews fail due to CRUD/FLS violations. The highlighted codelines include almost every SOQL Query in the application.  Our approach is usually as follows:   In case of displaying data on VF pages we either use sObjects fields or use the platform methods to check the accessibility of the fields In case of domain logic triggered by the user (e.g. by clicking a button on a VF page) we have a helper class that checks every field to be updated before doing the DML operation.   Up until recently this approach has worked fine (and passed pervious Security Reviews). As mentioned above the latest Security Review results seem to require us to check every field in a SOQL query for accessibility even if it is never displayed back to the user.    Let's suppose the following program flow as an example:   Query an object with some fields Perform some modification on said fields Perform an update on the sObject to save the modification using a helper class which checks for the required CUD/FLS rights for the modified fields   As I see it there is no need for checking field accessibility in step 1 in that case (since nothing is displayed back to the user and the dml operation is already protected). Is that correct or am I missing something? So is it really required to do an accessibility check for every SOQL Query in the code?  Another question would be how to handle background operations in that case like data purging. These have either to be running in system mode (which causes issues during the Security Review) or require the job to be started by a user with the appropriate access rights (which can be error prone and is not that user friendly). Is there any best practice regarding that.  Unfortunately I could not find a question targeting exactly that issue. Most of the questions I have found are related to how to perform that check (like  or ). So please apologize in case the question was already answered (I would really appreciate a link to the answer then).    Thanks for your time and help.  Mathias sftp: upload all files, directories and sub-directories contained in a folder On machine A I have the folder /home/a/  On machine B I have the folder /home/b/  I wish transfer all files, directories and sub-directories of /home/a in /home/b with sftp On machine A I tried the commands: sftp fibon82@machineB.com put /home/a/* /home/b/  but it doesn't work, i get the error message: &quot;skipping non-regular file /home/a/a1&quot;... [a1 is a sub-directory of a] How could I modify the put instruction? Thanks! :) EDIT: I solved using scp: scp -r /home/a/ fibon82@machineB.com:/home/b/ I updated a virtual machine running Ubuntu server 15.04 to the just released new stable 15.10.  There were no apparent problems, but after reboot the machine lost its network connection. lspci showed the correct card and lsmod proved that the driver had been loaded.  Hints about editing or removing /etc/udev/rules.d/70-persistent-net.rules did not succeed (still no network, no new file), the famous /lib/udev/write_net_rules did not even exist.  I don't have much clue regarding udev and systemd, so it took me some time to find in /sys/class/net that the network interface name changed. It became ens32, which was renamed from eth0. After I changed /etc/network/interfaces network communication was enabled again.  But - why does this happen at all? And if it happens, shouldn't the interfaces file be updated automatically?  Now that I deleted the virtual network card and created another one, eth0 becomes eno16777728, which is not so, uhm, nice.  Should this behaviour (at least that of the upgrade procedure) be reported as a bug?  Furthermore, is /etc/udev/rules.d/70-persistent-net.rules obsolete now? And (although only partly related) what about /etc/udev/rules.d/70-persistent-cd.rules?)  Edit - additional question (after accepted answer) The dependency of /etc/network/interfaces from the actual interface name bothered me. I tried a new installation of *ubuntu in another virtual machine. To my surprise, /etc/network/interfaces contained a reference to the loopback device only. However, with my original VM this change prevented the network to come up. So what else do I need to change?  Edit Well, from another test I found that a new Ubuntu Server has the network interface card in /etc/network/interfaces, while XUbuntu has not. Maybe it is using network-manager or something else. hotel occupancy counting problem The multiple-choice question:  A hotel has four vacant rooms. Each room can accommodate a maximum of four people. In how many different ways can six people be accommodated in the four rooms? (A) 4020 (B) 4068 (C) 4080 (D) 4096.  My attempt:  If there were no 'four person' constraint, the six people could be accommodated in $4^6=4096$ ways. however, this number includes combinations with 5 or 6 people in one room, which should be excluded.  If one room has 5 occupants, one other room has 1 occupant. The number of '1,5' combinations is ${{4} \choose {2}}$=12. If one room has 6 occupants, the other three rooms have no occupants, and there are four such combinations.  I believe the answer should be $4096-12-4=4080$, but am not confident. I'd be grateful for any comments on my attempt. Label equation with a symbol I would like to label an equation with an arbitrary symbol, rather than a number, or letter.  Is this possible? Can the manual and tome magic items that increase stats be used multiple times by bypassing the century wait time via the spell Sequester? Assume we have a Wizard who is at least level 13 and can reliably cast  many times (either through acquired spell scrolls, or has acquired enough material components for it to be a non-issue), has a safe place (through the spell ) to be under the influence of Sequester for many centuries, and has access to the Manual of Bodily Health, Manual of Gainful Exercise, Manual of Quickness of Action, Tome of Clear Thought, Tome of Leadership and Influence, and Tome of Understanding.  Per the item descriptions in the DMG:     ...your [STAT] score increases by 2, as does your maximum for that score. The manual then loses its magic, but regains it in a century.   Now, normally this would be a once-in-a-lifetime use, or maybe twice (due to the lifespan of the races), but if a wizard used Sequester on themself, many years can pass without growing older:     ...[willing target creature] falls into a state of suspended animation. Time ceases to flow for it, and it doesn't grow older. You can set a condition for the spell to end [before the spell is dispelled by the caster].   So, assuming that time continues to flow for the magic items, but not for the sequestered wizard, can they study these books and take the necessary long rests, Sequester for a hundred years,  “wake” from the Sequester, and then repeat an arbitrary-but-finite number of times for an arbitrarily high (but finite) improvement to their stats?  To end the cycle and escape the demiplane, the wizard would simply Plane Shift out:     ...You can specify a target destination in general terms ... and you appear in or near that destination. I'm trying to work with  in Java.   I want to implement arithmetic functions.  For this, I will first require a way to normalize the functions.  I know I can't add 1/6 and 1/2 until I have a common denominator. I will have to add 1/6 and 3/6.  A naive approach would have me add 2/12 and 6/12 and then reduce.  How can I achieve a common denominator with the least performance penalty?  What algorithm is best for this?    Version 8 (thanks to ):     Improvements include:         the equals() method is now consistent with the compareTo() method      final class Fraction extends Number {     private int numerator;     private int denominator;      public Fraction(int numerator, int denominator) {         if(denominator == 0) {             throw new IllegalArgumentException("denominator is zero");         }         if(denominator &lt; 0) {             numerator *= -1;             denominator *= -1;         }         this.numerator = numerator;         this.denominator = denominator;     }      public Fraction(int numerator) {         this.numerator = numerator;         this.denominator = 1;     }      public int getNumerator() {         return this.numerator;     }      public int getDenominator() {         return this.denominator;     }      public byte byteValue() {         return (byte) this.doubleValue();     }      public double doubleValue() {         return ((double) numerator)/((double) denominator);     }      public float floatValue() {         return (float) this.doubleValue();     }      public int intValue() {         return (int) this.doubleValue();     }      public long longValue() {         return (long) this.doubleValue();     }      public short shortValue() {         return (short) this.doubleValue();     }      public boolean equals(Fraction frac) {         return this.compareTo(frac) == 0;     }      public int compareTo(Fraction frac) {         long t = this.getNumerator() * frac.getDenominator();         long f = frac.getNumerator() * this.getDenominator();         int result = 0;         if(t&gt;f) {             result = 1;         }         else if(f&gt;t) {             result = -1;         }         return result;     } }     I have removed all previous versions.  My thanks to: Determine whether $712! + 1$ is a prime number or not Let $n = 712! + 1$ If $n$ was a prime number then, by Wilson's theorem:  $ (712!)! \equiv -1 \pmod{712}$  The double factorial makes it seriously more difficult...  But We can require:  $$712!! + 1 \equiv 0 \pmod{712}$$  $$712 = 2\cdot 356$$   Hence: $712!! = 2^{356} 356!$  Lets compute: $356! \pmod{712}$. Obviously:  $$356! = (356 \cdot 2) \cdot (355!/2)  = 712 \cdot 355!/2$$  Then: $356! \pmod{712} \equiv 0$.   Now, $2^{356} \pmod{712}$  $2^{356} = 2^{6 + 350}$  Nevermind, what should I do? Find the volume of rotation about the y-axis for the region bounded by $y=5x-x^2$, and $x^2-5x+8$  Here is an image:    Normally I can do this question, but this one is tricky because since we are rotating about the y-axis, and we are quadratic, when I solve for $x$ I get two answers, one positive and one negative.   What I mean is that if you look at the graph $5x-x^2$, then there are two halves, and if you look at the green line, that's one half of the curve (positive one), and the red half is the negative one.  Since we can see both the negative and positive sections in this graph, and both are being rotated, I wasn't sure how to create the equation that I can later integrate.  Usually in the problems I do, the negative doesn't exist, and so it's trivial. In this case I am not sure. How to get parent process in .NET in managed way I was looking a lot for method to get parent process in .NET, but found only P/Invoke way.