What is the chance...
Repeating something with (1/n)th chance of success n times
How to open and repair an m4v or mp4 video file? Yesterday I was filming a scene with my phone but suddenly the application crashed and when I try to open the m4v generated it says that is corrupted.  I have downloaded the video files (around 36MB) on my PC and I am trying to open and repair it. Can you suggest me a way to do it?  FFMPEG info  As suggested in comments I try check what FFMPEG says me about that file with this command  ffmpeg.exe -i VID_20120425_144739.m4v -c:v copy -c:a copy out.mp4 2&gt; log.txt   Here it is the result:  ffmpeg version N-40126-ga4b58fd Copyright (c) 2000-2012 the FFmpeg developers   built on Apr 26 2012 03:29:50 with gcc 4.6.3   configuration: --enable-gpl --enable-version3 --disable-w32threads --enable-runtime-cpudetect --enable-avisynth --enable-bzlib --enable-frei0r --enable-libass --enable-libcelt --enable-libopencore-amrnb --enable-libopencore-amrwb --enable-libfreetype --enable-libgsm --enable-libmp3lame --enable-libnut --enable-libopenjpeg --enable-librtmp --enable-libschroedinger --enable-libspeex --enable-libtheora --enable-libutvideo --enable-libvo-aacenc --enable-libvo-amrwbenc --enable-libvorbis --enable-libvpx --enable-libx264 --enable-libxavs --enable-libxvid --enable-zlib   libavutil      51. 47.100 / 51. 47.100   libavcodec     54. 15.100 / 54. 15.100   libavformat    54.  3.100 / 54.  3.100   libavdevice    53.  4.100 / 53.  4.100   libavfilter     2. 72.100 /  2. 72.100   libswscale      2.  1.100 /  2.  1.100   libswresample   0. 11.100 /  0. 11.100   libpostproc    52.  0.100 / 52.  0.100 [mov,mp4,m4a,3gp,3g2,mj2 @ 003fc940] moov atom not found VID_20120425_144739.m4v: Invalid data found when processing input   Latest two lines are displayed in red. When it's OK to omit "where?" If the laws of random variables weakly converge to a point mass at $c$, then the random variables converge in probability to $c$. This is question 10.3.1 from Rosenthal's First Look at Rigorous Probability.  Suppose $\mathcal{L}(X_n) \Rightarrow \delta_c$ for some $c \in \mathbb{R}$. Prove that $\{X_n\}$ converges to $c$ in probability.  Here $\mathcal{L}(X_n)$ refers to the distribution of $X_n$.  Is the following proof correct?  Is a simpler proof available?  Is there a simple proof using Skorohod's theorem?  I attempted to prove the contrapositive. Suppose $X_n \not \to c$ in probability.  This means that there is an $\varepsilon &gt; 0$ so that for all $N$, there exists an $m &gt; N$ such that  \begin{equation}   P(|X_m - c| \geq \varepsilon) &gt; \eta, \text{ for some $\eta &gt; 0$}. \end{equation}  Consider  \begin{equation}   B := \{x \in \mathbb{R} : |x - c| \leq \varepsilon\} \in \mathcal{B} \text{ the Borel sets on $\mathbb{R}$}. \end{equation}  Then $B^c \in \mathcal{B}$ and denoting the distribution of $X_n$ as $\mu_n$ we have  \begin{equation}   \mu_n(B^c) = P(X_n \in B^c) = P(|X_n - c| \geq \varepsilon) &gt; \eta. \end{equation}  For all $N$, there exists an $m &gt; N$ such that the cumulative distribution function of $X_m$ is not the same as the cumulative distribution function of $\delta_c$; in particular it's mass changes somewhere at least $\varepsilon$ distance from $c$. Finally because $\delta_c(\{x\}) = 0$ for all $x \neq c$ this completes the proof. Word for the satisfaction of curiosity There is a good feeling you get when your curiosity is satisfied, especially if is about a question you found interesting or important, or have spent a lot of time and energy trying to answer. Depending on how much I wanted to know, this feeling can be quite pleasing. Is there a word specifically for either the satisfaction of a curiosity, or the feeling that results? As a non-native speaker, I cannot grasp any difference between the expressions "here we go" and "there we go": both expressions seem to underline an event that is going to happen immediately.  Is there any subtle usage detail that I am missing? Does $1.0000000000\cdots 1$ with an infinite number of $0$ in it exist? Does $1.0000000000\cdots 1$ (with  an infinite number of  $0$ in it) exist? When installing user applications, where do "best practices" suggest they be located? Occasionally I install applications manually, rather than using apt or another package manager.   What location (/usr/, /usr/local/, /opt/, /home/, etc.) is suggested by "best practices" for the installation of user applications? A message may be accompanied with a digital signature, a MAC or a message hash, as a proof of some kind.  Which assurances does each primitive provide to the recipient?  What kind of keys are needed? Synchronize Clocks I need to develop a system where there are 4 sensor boxes powered by USB and they have their internal clock. Each of these boxes are connected to a Linux pc and all these PCs are linked with WiFi. API of the sensor box allows me to read their internal precision clock (uSec accuracy).   I like to synchronize all four clocks of the sensor boxes as close as possible. Hopefully within a few micro seconds of each other and compensate for drift over time. The idea is to use the sensor data that is collected at the same time (The data I receive is time stamped with the boxes' internal clock). The latency on usb bus, WiFi, pc timing are all indeterministic.  Is this possible given my setup? Sentence vs proposition I'm reflecting upon the distinction between a sentence and a proposition in logic and philosophy. I knew that a proposition is the meaning of a declarative sentence (i.e. the abstract content of a declarative sentence, the bearer of truth-value), whereas a sentence is simply a group of words (symbols, signs) ordered according to some grammatical rule in any natural or artificial language. A sentence isn't necessarily meaningful.   According to these definitions, you could say hat a predicate like "is interesting" is a sentence. Of course a sentence like "is interesting" wouldn't express a proposition, but still, it would be a sentence. This seemed ok to me until I remembered that propositional logic is sometimes called sentential logic. But then you cannot say that "is interesting" is a sentence, because it certainly isn't a sentence in the sense of sentential logic! As a result, I'm getting confused about what a sentence is according to sentential logic.   Can someone help? Why is "can I get" replacing "could I have"? I noticed the other day when serving the public that when asking for something, people were saying "Can I get an xyz, please". The previous time I had such a job it was "Could I have an xyz", or "May I have..." if they were being very polite.  Does anyone know when this trend started and what caused it? How do I effectively defeat the Wall of Flesh? I've been having trouble defeating this monster. Even with lots of buff potions, health potions, high tier armor (Molten), and ranged weapons with plenty of ammo (Minishark), I can't seem to kill this boss.  Worse, when I get it down to about 2000 hp, even if I'm fairly far away, it'll suck me in and continually rise towards the skybox, which doesn't allow me to do anything for some reason.  How do I defeat the Wall of Flesh? What gear should I be using and what kind of potions do I need? Negative integer division surprising result Where can I find other RPG players? How do I find the index of an element in a list in Racket? Verbatim Environment in Figure Caption verbatim environment is not working in figure caption. Checked  and  is not working.  \documentclass[11pt, double space]{article} \usepackage{amsmath} \usepackage{graphicx} \usepackage{color} \usepackage[usenames,dvipsnames]{xcolor} \usepackage[english]{babel} \usepackage[autostyle, english = american]{csquotes} \MakeOuterQuote{"} \usepackage{cprotect}  \begin{document} \begin{figure}[!h] \caption{Sample 1 \cprotect\begin{verbatim} \tau(A) = e^{\chi_0A/(KD_p(K+A))} \end{verbatim} per hour.} \label{fig:singlecell_chemo} \end{figure}  \end{document}   I have tried cprotect package also. Any help. I noticed that if I run ls -F on a directory, some of the entries have a * or a @ after them.   spuder@ubuntu:~$ ls -F /sbin acpi_available*   getpcaps*           lvmconf*                 ntfscp*        start-stop-daemon* agetty*           getty*              lvmdiskscan@             ntfslabel*     status@ alsa*             halt@               lvmdump*                 ntfsresize*    stop@ alsactl*          hdparm*             lvmsadc@      spuder@ubuntu:~$ ls -F ~ daq-0.6.1/  examples.desktop       noname-cache.lib  snort-2.9.1/   Templates/ Desktop/    jpgraph-1.27.1/        noname.sch        snortfiles/    Ubuntu One/ Documents/     According to the ls man pages   spuder@ubuntu:~$ man ls ... -F, --classify   append indicator (one of */=&gt;@|) to entries ...   I'm guessing that @ means symbolic link,     What do these other indicators mean ( */=&gt;@| )  ? Converting LiDAR files from LAZ to LAS format I'm trying to convert LiDAR files from the LAZ format (the compressed version) into LAS (the uncompressed version) using  software.   However, I am not really sure how it works. I created a new output folder as I entered in the app interface, but it is totally empty.  I also had tried the following code in the command prompt window:   D:\LiDAR\Laszip\laszip.exe *.laz    and got a message saying 'no input specified'.  In my folder, there are about 100-ish.laz files as well as one imu.laz. Any suggestions? Is there a way in javascript to detect if the unload event is caused via a refresh, the back button, or closing the browser? Javascript variables keep track to their copies?