I am trying to estimate the (say 95%) confidence interval of a proportion. For instance, I want to estimate how many students will take a particular course next year. There are N1 students in total. I asked randomly N2 students, and N3 students say yes. I estimate the proportion is N3/N2. I tried to estimate the confidence interval as:  Source:  However, if p' is 0 or 1, how could I calculate the standard deviation because it will become 0, regardless of the sample size?
What is the best technique to calculate a confidence interval of a binomial experiment, if your estimate is that $p=0$ (or similarly $p=1$) and sample size is relatively small, for example $n=25$?
Upgrade to the latest PHP version in Ubuntu Is a semigroup with unique right identity and left inverse a group? I created a bunch of filters in Gmail for a "master account" that receives forwarded mail from all of my accounts.  The filter list and web of labels/folders has grown to be rather long, and therefore a bit burdensome to manage. I would like to edit / delete / consolidate a lot of these filter rules (and folders) but it seems the only way I can interface with them is through the laundry list at Setting/Filters. It'd be cool there was an option to "View/Edit Filter" on an individual email's page, but I'm not sure if something like that currently exists.  What's the best way to view a filter rule currently being applied to an email (in Gmail)? Determine $4$ specific digits in $34!$ Find the values of $a,b,c,d\in\mathbb{N}$ such that      $$ 34!=295232799cd9604140847618609643ab0000000 $$   My Attempt:  The factorial of $34$ contains a $3$, so the RHS must be divisible by  $3$. Similarly, it must be divisible by $7$, $11$, $13$, $19$ etc.  But I do not understand how can I calculate $a,b,c,d$ in this equation. When I apply to a PhD program, may I ask a postdoc who closely supervised me to write a recommendation letter? My supervisor also has written one for me, but I believe the postdoc can comment on my research skills in a more detailed and precise way. Does a postdoc have enough authority to convince admission committee? Installing python module within code Is there a difference between installing an application via Ubuntu Software Center or a terminal? I would like to ask a very basic question but I have never thought about it before. Well, when someone installs an application from terminal, he has to add the repository first, right? On the other side, when someone installs an application from the Ubuntu Software Center, is the repository then added automatically?  I am asking those questions to figure out this: When I run update and then upgrade, will this application be upgraded or not? Is the result same in two options? How do I troubleshoot the "Error, press shutter release button again" message on my Nikon? The LCD on my Nikon D3000 is displaying the following error message:     Error. Press shutter release button again.   I have pressed the shutter release button but the camera still does not work. Two layers, same coordinate system, wont show up I have vector two sets of vector layers that won't show up together. One set shows up together and the other set together etc but they are of the same area.  The layers I was given did not have a defined spatial reference which I manually projected as the same as the data frame I specified so all layers now have same CRS...yet not showing up together. I have noticed they appear to have different extents... What should I do? What's the current state of LaTeX3 (2020)? There are a few questions on this forum asking about why Latex3 is taking so long to come out. However, all of these are from the early 2010s. I'm just wondering what the current state of the project is and whether it's ready (or nearly ready) for prime time? Lost email settings and no icon for Mail I've lost my Settings → Mail, Contacts, and Calendars on my iPhone 5.  No icon for Mail and no Mail settings.  How do I get it back? How to update kernel to the latest mainline version without any Distro-upgrade? So I was playing around on Area 51 hoping for further news on the private beta for ebooks, and noticed that my avatar (a hand) was missing. Also the Area 51 has the old toolbar. So I looked at the flair page. The network flair has my hand, the Area 51 flair has a quilt. OK, so time to upload a new image, and WordPress -- WordPress -- I don't want to login to WordPress. Any idea what's up with that?  The following questions did not help, and have different causes and symptoms: Possible Beamer bug: Frame number has different color than date in infolines footer How to count number of words from String using shell 4 cards are drawn from a pack without replacement. What is the probability of getting all 4 from different suits?  Here's how I tried to solve:  For the first draw, we have 52 cards, and we have to pick one suit. So, probability for this is $\frac{13}{52}$.  For the second draw, only 51 cards are left. The second suit has to be selected, so there are 13 cards from that suit. The probability is $\frac{13}{51}$.  Similarly, the third and fourth draw have probabilities $\frac{13}{50}$ and $\frac{13}{49}$ respectively.  Since the draws are independent, the total probability becomes $$\frac{13}{52} \times \frac{13}{51} \times \frac{13}{50} \times \frac{13}{49}$$  But my book says the answer is $\frac{{13\choose 1} \times {13 \choose 1} \times {13\choose1} \times {13\choose1}}{52 \choose 4}$.  My answer differs by a factor of $4!$. What did I do wrong? Correct spelling of Polish surname Dziubenofska? My Polish grandmothers last name was Dziubenofska, but I know that's not how it is spelt! I'm looking for the proper spelling.   Can you help find it for me?  She came over to Ellis Island and they changed it on her to dziuk. This is only a prefix to the full name. I am trying to implement the following K-map with a table    AB C     00 01 11 10       ______________     0| 1  0  1  0     1| 0  1  1  0   I implemented it like this:   \begin{table}[htdp] \begin{center} \begin{tabular}{c|c|c|c|c|}  &amp;00 &amp; 01&amp; 11&amp; 10 \\ \hline 0&amp;1&amp;1&amp;1&amp;1\\ 1&amp;0&amp;0&amp;0&amp;0\\ \end{tabular} \end{center} \label{default} \end{table}   However on the top row I have vertical lines that I'd like to not see. I went with this approach because if i was to use a one row with the information so that I wouldn't have to worry about aligning the headings. So is there a way I can get the vertical lines not to appear in the heading row? How to view the output of a running process in another bash session? I have left a script running on a remote machine from when I was locally working at it. I can connect over SSH to the machine as the same user and see the script running in ps.   $ ps aux | grep ipcheck myuser  18386  0.0  0.0  18460  3476 pts/0    S+   Dec14   1:11 /bin/bash ./ipchecker.sh   It is simply outputting to stdout on a local session (I ran ./ipchecker.sh form a local terminal window, no redirection, no use of screen etc).  Is there anyway from an SSH session I can view the output of this running command (without stopping it)?  So far the best I have found is to use strace -p 18386 but I get hordes of text flying up the screen, its far too detailed. I can stop strace and then sift through the output and find the text bring printed to stdout but its very long and confusing, and obviously whilst it's stopped I might miss something. I would like to find a way to see the script output live as if I was working locally.  Can anyone improve on this? The obvious answer is to restart the script with redirection or in a screen session etc, this isn't a mission critical script so I could do that. Rather though, I see this as a fun learning exercise. What is the difference between "du -sh *" and "du -sh ./*"? What's the difference between du -sh * and du -sh ./* ?  Note: What interests me is the * and ./* parts.