What can we say about $\mathbb{E} \left(\frac{1}{\sum_{i=1}^N X_i}\right)$?
Inverse of sum of exponential random variables (mean and variance)
Parametric Form for a General Parabola It is well known that a parametric form of the parabola $y^2=4ax$ is $(at^2, 2at)$.      What are possible parametric forms of the general parabola   $$(Ax+Cy)^2+Dx+Ey+F=0$$   ? A question about long exact sequence of finite dim vector spaces How to center text vertically within a textbox in Photoshop Placement of images in row using subfigure I want to put four figures in a single row. The code I am trying to use is taken from .  This puts three figures in a row. When I add a fourth one, I get three images in row and the last one appears in the second row. But I want all of them in one row. Here is my code.  \documentclass[12pt,twoside]{report}% Use this line for the print version of the thesis   \usepackage{graphicx} \usepackage{caption} \usepackage{subcaption} \begin{document}  \begin{figure}         \centering         \begin{subfigure}[b]{0.3\textwidth}                 \centering                 \includegraphics[width=\textwidth]{gull}                 \caption{A gull}                 \label{fig:gull}         \end{subfigure}%           \begin{subfigure}[b]{0.3\textwidth}                 \centering                 \includegraphics[width=\textwidth]{gull}                 \caption{A gull2}                 \label{fig:gull2}         \end{subfigure}%          ~ %add desired spacing between images, e. g. ~, \quad, \qquad etc.           %(or a blank line to force the subfigure onto a new line)         \begin{subfigure}[b]{0.3\textwidth}                 \centering                 \includegraphics[width=\textwidth]{tiger}                 \caption{A tiger}                 \label{fig:tiger}         \end{subfigure}         ~ %add desired spacing between images, e. g. ~, \quad, \qquad etc.           %(or a blank line to force the subfigure onto a new line)         \begin{subfigure}[b]{0.3\textwidth}                 \centering                 \includegraphics[width=\textwidth]{mouse}                 \caption{A mouse}                 \label{fig:mouse}         \end{subfigure}         \caption{Pictures of animals}\label{fig:animals} \end{figure} \end{document}   As I have mentioned above, it works for three figures.  But I can not use it for four figures. What should I change?   What does  width=\textwidth mean?   I changed    \begin{subfigure}[b]{0.3\textwidth}   to  \begin{subfigure}[b]{0.2\textwidth}   but it didn't help.  Then, I changed     \includegraphics[width=\textwidth]{mouse}   to  \includegraphics[width=0.5\textwidth]{mouse}   Still no solution. In the simple linear regression case $y=\beta_0+\beta_1x$, you can derive the least square estimator $\hat\beta_1=\frac{\sum(x_i-\bar x)(y_i-\bar y)}{\sum(x_i-\bar x)^2}$ such that you don't have to know $\hat\beta_0$ to estimate $\hat\beta_1$  Suppose I have $y=\beta_1x_1+\beta_2x_2$, how do I derive $\hat\beta_1$ without estimating $\hat\beta_2$? or is this not possible? How to prove $|a+b|^k \leq 2^{k-1} (|a|^k+|b|^k)$? Assume that you have any two real numbers $a$ and $b$, and $1\leq k &lt;\infty$, $k \in \mathbb{R}$.  How would you prove the inequality $|a+b|^k \leq 2^{k-1} (|a|^k+|b|^k)$? Get list of all tables in Oracle? Best way to simulate "group by" from bash? Indicate How Trustworthy the UpVotes Are A 2x2 matrix $M$ exists. Suppose $M^3=0$ show that (I want proof) $M^2=0$ How $\frac{1}{n}\sum_{i=1}^n X_i^2 - \bar X^2 = \frac{\sum_{i=1}^n (X_i - \bar X)^2}{n}$ How   $\frac{1}{n}\sum_{i=1}^n X_i^2 - \bar X^2 = \frac{\sum_{i=1}^n (X_i - \bar X)^2}{n}$   i have tried to do that by the following procedure:  $\frac{1}{n}\sum_{i=1}^n X_i^2 - \bar X^2$  =$\frac{1}{n}(\sum_{i=1}^n X_i^2 - n\bar X^2)$  =$\frac{1}{n}(\sum_{i=1}^n X_i^2 - \sum_{i=1}^n\bar X^2)$  =$\frac{1}{n} \sum_{i=1}^n (X_i^2 - \bar X^2)$  Then i have stumbled. Find all solutions of the equality $y^2=x^3+23$ for integers $x,y$   I guess, that x cannot be even. because we can apply mod 4 test  say $x=2k$ then $y^2=8k^3+23\equiv3\mod(4)$   but, this is not possible, since the square of an integer is congruent to $0$ or $1$ $\mod (4)$  so $x$ is of the form $4k+3$ or $4k+1$  $x=4k+3$ is also not possible for the same reason but for the last case the test fails.  any hints ? WPF CommandParameter is NULL first time CanExecute is called The drive is constantly filling up. You've hunted down all the spare and random files you can. grep'd for coredump files and even removed some of the un-needed backups...  What would be your next move.  The actual server in question has 10GB of website files and the OS shouldn't take any more than 10GB so how do you track down what's filling a 50GB (virtual) drive? How do i renable connecting a network drive using SMB1 since Windows 1709 I find today that I can no longer mount my Netgear ReadyNas drive because apparently it is using SMB1 and Windows 10 have disabled since release 1709. This is very problemaic because I need to access these files and because I have lost the admin password for the ReadyNas itself so I cannot login in order to update/reconfigure it to use SMB2 instead.  Microsoft refers me  to  which in turn refers me to  if I really want re-enable SMB1  And I successfully did re-enable SMB1 by running  Enable-WindowsOptionalFeature -Online -FeatureName smb1protocol   from Powershell as Adminstrator.  However even after reboot I still cannot re-establish connection to my Netgear from Windows Explorer, it gives the same error  What else do I need to do ?  PS C:\WINDOWS\system32&gt; Get-WindowsOptionalFeature –Online –FeatureName SMB1Protocol   FeatureName      : SMB1Protocol DisplayName      : SMB 1.0/CIFS File Sharing Support Description      : Support for the SMB 1.0/CIFS file sharing protocol and the Computer Browser protocol. RestartRequired  : Possible State            : Enabled CustomProperties :                    ServerComponent\Description : Support for the SMB 1.0/CIFS file sharing protocol and the Computer                    Browser protocol.                    ServerComponent\DisplayName : SMB 1.0/CIFS File Sharing Support                    ServerComponent\Id : 487                    ServerComponent\Type : Feature                    ServerComponent\UniqueName : FS-SMB1                    ServerComponent\Deploys\Update\Name : SMB1Protocol   Solution  Thanks Bob, SMB 1.0/CIFS File Sharing Support was enabled but within it SMB 1.0 Client was not enabled, checking that box and rebooting fixed the issue. How can you get the permalink for an answer to a question? I wanted to link to an answer to a Stack Overflow question, but couldn't find a way to do it. I couldn't get the ID of the answer in order to create the link.  How can you get the permalink for an answer to a question? An easy bash completion tutorial? How should I address a potential FERPA violation by a professor? In the United States, federal law prohibits professors from releasing any student's grades to any party other than the student and any party whom the student authorizes to receive the grades.  One of my professors appears to be violating this law by uploading each student's lab grades in one file, which is accessible to anyone who is enrolled in the class.  Here is my proposed plan of action:   Ask the professor - in private - to post the grades using the online management system the professor already uses for other things.  If the professor doesn't fix this privacy violation, inform the professor that the method by which he/she post grades is a violation of federal law. As a last resort, contact the department dean. Saying that refers to not going overboard in solving a problem when a simple solution exists So I know I've heard this saying in American English before but I just can't quite find the original.  I have come up with several made up variations like:   I don't send the Navy (or whole army, or a battalion) when all you need is a diplomat. Don't buy the whole cow when all you need is milk.   What's the more commonly heard saying/phrase for this of expression? Add a downvote option in the VLQ review There are many answers that are well-formed and well-formatted but are simply plain wrong or misleading. When reviewing, I often have a hard time deciding which action to take, as:   Looks Good: is OK per se but I would never say "good" (would work if the wording was changed slightly), Edit: The question is formatted well and editing it to be right would go against the intent of the author, Recommend deletion: this looks like the most reasonable choice, but I wouldn't flag it if I were browsing the site in normal mode, Not sure: I am quite sure what is wrong but I end up clicking this because the other three options do not seem fitting.   My proposal is to add a fifth option - Downvote that would make it easier to choose in case of such answers.