I was looking at a question shown for the  on English Language Learners, and noticed the "add comment" link was disabled because I needed at least 50 points of reputation.    As the screenshot shows, my reputation is more than 50.  The link should not appear, if commenting is not allowed, or I should be allowed to comment.
When reviewing an answer in the low quality queue the question doesn't believe that I have enough reputation to comment.        I can't remember if commenting on the post not actually being reviewed was ever allowed?
Show that $\mathbb{E}(T) = \sum\limits^\infty_{k=1}\mathbb{P}(T \geq k)$ for $T$ nonnegative integer valued and $E[T] < \infty$ Let T be a non-negative integer-valued random variable with $\mathbb{E}(T) &lt; \infty $. Prove that $\mathbb{E}(T) = \sum^\infty_{k=1}\mathbb{P}(T \geq k)$.  Had a few attempts, haven't really got anywhere. I'm wondering as I'm typing this if proof by induction is a good way to go.  Edit: One major thing I forgot to add, am I correct in thinking that also, $\mathbb{E}(T) = \sum^\infty_{k=1}k\mathbb{P}(T = k)$? pgfplots: prevent single plot from being listed in legend In order to fill the area between two complex curves I use tables and the vertcat command (see ).   Now I don't want the plotted area to appear in my legend, just the two curves. Is there any command to prevent the yellow area plot from being added to my legend?  this could be a minimal example:  \documentclass{article} \usepackage{pgfplots}  \begin{document} \begin{tikzpicture}   \begin{axis}[area style,axis on top]     \addplot+[mark=none,fill=yellow,draw=none] {0.1*x^2} \closedcycle;     \addplot[mark=none,draw=red,line legend] {0.1*x^2};     \addplot[mark=none,draw=blue,line legend] {0.0*x^2};     \legend{red curve,blue curve};     % \legend{\empty,red curve,blue curve};   \end{axis} \end{tikzpicture} \end{document}   With this legend{...}-command the last plot is skipped, an additional \empty doesn't help, too.  Sadly, drawing the first to plots together with fill=yellow,draw=red is not an option for me. Does anybody know any inside hacks? As far as I know, there is no command shown in the manual. Thanks in advance. Does someone knows if it exists some ppa packages source for the newest Ubuntu version 19.10 i had problem with that when i upgraded from Ubuntu 19.04 to 19.10 i didn't work? My USB drive used to be originally 8GB when I bought it.  I'm trying to reformatted in Windows 7 by right clicking on the drive and selecting Format.... But the capacity only shows 250MB.  Is there something I can do to get the original size back? Maybe it got partitioned in a weird way?   The  flash drive is a SanDisk Cruzer Micro 8GB. I got it from Wal-Mart but this is the same drive. Integer solutions to the equation $a^3+b^3+c^3=30$ How can I make a procedural polished granite material? I'm reading through a proof in my lecture notes:     Every convergent sequence of a metric space has a unique limit.   Suppose $\lim_{n \to \infty} x_n = l$ and $\lim_{n \to \infty} x_n = m.$ Then for every $\epsilon &gt; 0,$ there exists $N$ such that for every $n \geqslant N,$  $$d(l,m) \leqslant d(l,x_n) + d(x_n,m) &lt; \epsilon + \epsilon = 2 \epsilon. $$  So $(\star) \hspace{1mm} 0 \leqslant \frac{d(l,m)}{2} &lt; \epsilon \Longrightarrow \hspace{1mm} (\star^\prime) \hspace{1mm} \frac{d(l,m)}{2} =0 \Longrightarrow l = m.$  I can follow the proof up until the jump from $(\star)$ to $(\star^\prime)$. Why does $\frac{d(l,m)}{2}=0$? WPF TextBox and Scroll behavior I have a problem. I need to host grid with controls in ScrollViewer to prevent textbox from being either truncated or collapsed to zero-with at the UI. Also I want the with of textbox to be expanded when user change windows width. I'm setting Window's content to following code  &lt;DockPanel&gt;     &lt;TreeView DockPanel.Dock="Left" Width="150"/&gt;     &lt;ScrollViewer VerticalScrollBarVisibility="Auto" HorizontalScrollBarVisibility="Auto"&gt;         &lt;Grid&gt;             &lt;Grid.ColumnDefinitions&gt;                 &lt;ColumnDefinition Width="Auto"/&gt;                 &lt;ColumnDefinition /&gt;             &lt;/Grid.ColumnDefinitions&gt;             &lt;Grid.RowDefinitions&gt;                 &lt;RowDefinition Height="Auto"/&gt;             &lt;/Grid.RowDefinitions&gt;             &lt;TextBlock Text="Name"                         Margin="5"                         VerticalAlignment="Center"/&gt;             &lt;TextBox Grid.Column="1"                      Text="Some Name"                      Margin="5"                      VerticalAlignment="Center"                      MinWidth="200"/&gt;         &lt;/Grid&gt;     &lt;/ScrollViewer&gt; &lt;/DockPanel&gt;   All work fine, but when user types very long text in TextBox it is being expanded and horizontal scroll appears. Is there any easy way to limit TextBox maximum width and allow it to be expanded only when user changes window size. I'm trying to install , an open-source Microblogging application on my Windows development server using XAMPP as per the . The website cannot find PEAR, and throws the below errors:  Warning: require_once(PEAR.php) [function.require-once]: failed to open stream: No such file or directory in C:\xampplite\htdocs\laconica\lib\common.php on line 31 Fatal error: require_once() [function.require]: Failed opening required 'PEAR.php' (include_path='.;\xampplite\php\pear\PEAR') in C:\xampplite\htdocs\laconica\lib\common.php on line 31   PEAR is located in C:\xampplite\php\pear phpinfo() shows me that the include path is .;\xampplite\php\pear  What am I doing wrong? Why isn't the PEAR folder being included? How do I calculate number of hours > 24 in Excel? I've got an excerpt of my spreadsheet below. It's a time tracking application containing a start date/day, a session ID and the duration of the session. Column A is populated by adding the duration in Column D. I'm trying to total the durations, but keep getting incorrect values in cases where the total duration is > 24 hours.  Consider        A                   B        C                D          1  2012/05/22 01:00  |  Wed  |  Session 23341  |  9:00 2  2012/05/23 10:00  |  Wed  |  Session 23342  | 22:00 3  2012/05/25 08:00  |  Fri  |                 |  0:00   As you can see, the date differential between A2 and A3 demonstrates that the value of 22:00 in D2 represents a duration of 46 hours (05/23 10:00 + 46:00 = 05/25 08:00). However, Column D is only displaying the 22:00 in excess of a full 24 hour day.  My attempts to read D2 have included int(d2) = 0.00  /  int(d2)*24 = 0.00  /  hour(d2) = 22.00  /  int(a3-a2)*24 =0.00 etc. and have been unsuccessful in pulling a value of "46".   How can I accurately represent D2 to achieve accurate summary data? Concatenating numbers and adding in leading zeros? I have three text fields populated as follows: 1, 9, 1 that I need to concatenate into a field that looks like 01.09.01.  Getting to 1.9.1 is easy but can anyone help out with how to formulate it so that each value has two places (i.e. add in those zeroes).  I used to do this in Excel but can't figure out how to work in ArcMap 10. Fix for Hibernate error "Use of the same entity name twice" How you fix the following Hibernate error:  What does "Use of the same entity name twice". How do I disable search-as-you-type text in Ubuntu 17.10 and later? I cannot find enable-interactive-search in    gsettings set org.gnome.nautilus.preferences enable-interactive-search true.     I searched using    gsettings list-recursively | grep search     and    gsettings list-recursively | grep interactive     but no such option.  Can you help me disable this in Ubuntu 17.10 and later? Laptop water damage repair procedure I'd love some advice in repairing a water-damaged laptop.  My girlfriend spilled a glass of water on her Sony Vaio and now it doesn't turn on...at all...dead! What steps should I go through to work out where the problem is and which part(s) I'll need to replace?  I can't seem to find out what has happened by just looking at the circuit boards. I'm new to electronics but could buy relevant volt-meters etc. I'm just looking for a decent trouble-shooting guide. These questions are really bothering me. Any help would be much appreciated.  Let $p$ be prime  a) If $(G, \oplus)$ has order $2p$, prove that every proper subgroup of $(G, \oplus)$ is cyclic  b) If $(G, \oplus)$ has order $p^2$, prove that $(G, \oplus)$ has a subgroup of order $p$ SQL to LINQ Tool Is there a tool out there which can convert SQL syntax to LINQ syntax?   I just want to rewrite basic queries with join, etc., to . It would save me a lot of time. How to hide terminal output when executing a command? Showing $\gcd(2^m-1,2^n+1)=1$ Maximum Likelihood Estimation (MLE) in layman terms Could anyone explain to me in detail about maximum likelihood estimation (MLE) in layman's terms? I would like to know the underlying concept before going into mathematical derivation or equation. Show that the set of all finite subsets of $\mathbb{N}$ is countable.   I'm not sure how to do this problem. I keep trying to think of an explicit formula for 1-1 correspondence like adding all the elements in each subset and sending that sum to itself in the natural numbers, but that wouldn't be 1-1 because, for example, the set {1,2,3} would send to 6 and so would the set {2,4}.  Multiplying all the elements in each subset and sending that product to itself in the natural numbers wouldn't work either since, for example, {2,3} would send to 5 and so would the set {1,5}. Any ideas?