Regular Expression (match integer at specific line) json
Learning Regular Expressions
Why is the observable universe so big? Convergence in Distribution in Order Statistics Let $X_1, X_2, \ldots$ be iid from Exp$(\theta)$ with density function $f(x) = \frac{1}{\theta}e^{-\frac{x}{\theta}}$. (a) Find the limiting distribution of $M_n = Y_1 - \theta\ln(n)$ and $T_n = nY_n$, where $Y_1$ and $Y_n$ represent the first and last order statistics (among $n$ observations) respectively. Answer: I have obtained the CDF of X to be: $$F_x(x) = 1 - e^{-\frac{x}{\theta}}$$ the CDF of $Y_1$ to be: $$F_{Y_1} = 1 = e^{-\frac{xn}{\theta}}$$ the CDF of $M_n$ to be: $$F_{M_n}(x) = \left[1 - \frac{1}{n}e^{-\frac{x}{\theta}}\right]^n$$ with limiting distribution $$e^{-e^{-\frac{x}{\theta}}}$$ the CDF of $T_n$ to be: $$F_{T_n}(x) = 1 - e^{-\frac{x}{\theta}}$$ which is also the limiting distribution. (b) Show that $M_n$ and $T_n$ are asymptotically independent. Answer: I've tried finding the joint PDF for ordered statistics by using the equation $$g_{ij}(y_i, y_j) = \frac{n!}{(i - 1)!(j - i - 1)!(n - j)!}[F(y_i)]^{i - 1}[F(y_j) - F(y_i)]^{j - i - 1}[1 - F(y_j)]^{n - j}f(y_i)f(y_j)$$ however, it is a mess based on my CDFs. Any suggestions on a different approach? Does a surjective ring homomorphism have to be surjective on the unit groups? What's the meaning of 90-plus? What's the meaning of 90-plus? More than 90? If so, please tell me more ways to say "more than 90". Thank you! I would like to set my monitor's scale under 100%, but Win10 only lets me set it to 100% or higher. Why won't Windows let me do that? Is there any workaround to do that? I am aware of the fact that scaling below 100% will result in merged pixels. Currently, for all my commands that require root access, I have to type them out on a command line.  I would like for the GUI to prompt me to key in my password, when sudo is required, instead of having to type out the commands from command line.  Is there any way to enable this? Previously one version of Ubuntu desktop had this feature out of the box.  This version of Ubuntu (that I am now running) I upgraded from a server installation.  I will add, my user account is already added to sudo group. Thus I can run commands such as sudo gedit or sudo apt-get but I'm not able to install software in the Ubuntu Software Center. My question is pretty simple.  Since $n! \gt n!!$, it's clear by the comparison test that $\sum_{n=0}^\infty \frac {1}{n!!}$ converges.      But what value does the sum converge to? How does one go about determining its value (if possible)? Let $g_n= {2^2}^n +1 $. Prove $g_0 · g_1 · · · g_{n−1} = g_{n} − 2$.    I'm not sure how to start this proof, if it should be done algebraically or if I should try to use a proof by induction. Find The Last 3 digits of the number $2003^{2002^{2001}}$ Find The Last 3 digits of the number $2003^{2002^{2001}}$  BY number theory or otherwise,   Also i would like to ask is there a property observed in the numbers of the form $k^n$, where for some $k, n$ is varied then the digits of $k^n$ are periodic,  for example,  $2^n$,  its last digit is periodic with period 4, its second last digit is periodic $4\cdot 5 = 20$ its third last digit is periodic with periodic with period $20\cdot 5 =100$  I have observed this property with other numbers as well, though period might vary,for different values of $k$. Where is the Layers panel in Blender 2.8? Why do the humans become sleepy after meals? macOS: Is there a way to show an image constantly on screen (like a watermark)? I'm looking for a very simple way to add a watermark to my screen which should be shown whatever I'm doing, is it during a Zoom call, or is it when giving a presentation, or similar (I don't necessarily need it to show during fullscreen mode). The reason is that I want to record my screen using QuickTime Player, and the watermark should be on the video. I know that there are many post-production tools that offer adding watermarks, but I don't want to do any post-production, I want to have everything on screen while recording already. (I also know that there are screen recorders which offer placing a watermark to the end result. I'd rather also avoid using another screen recording software, but if I don't find any other way to do it, then I'm open to a simple, non-pricy alternative to QuickTime Player.) Show that the range of $p(z)e^{q(z)}$ for nonconstant polynomials $p$ and $q$ is all of $\mathbb{C}$. Can we have a moderator only "flag for community team/developer attention" link on posts? There are times when moderators come across things that only Stack Exchange employees can deal with. These include things like deleting sensitive information permanently from posts disassociating users from posts that require direct database access.  (The previous use case is now possible for moderators to do directly the moderator redaction tool)  Currently the workflow is:   See the post (either in normal site usage or via a flag) Go to chat Ping one of the community team (if they are around) Explain the problem   A far better workflow for the moderator would be to simply able to flag the post so it then appeared in an "employee only" queue somewhere. This could either be a page on the main Stack Exchange site or (better still) their inbox.  (OK I admit I hadn't fully thought this last bit out.)  This could either be a moderator "flag to devs" link on the post or a new option on the existing flag dialog (probably the better solution).  Now that moderators can't merge we have a fairly common situation where this would be very useful. A new users posts an answer (or question on sites that don't require registration) then loses their cookies and ends up creating another unregistered account (or two). Eventually the might even create a registered account. It used to be easy to merge the unregistered accounts into the registered ones, but now we either have to badger the OP to use the "merge accounts" form or ping the team somehow.  Having the "flag for team" option would be very useful in this scenario. How do you prove the set $G = \{(x, f(x)) \mid x \in \mathbb R\}$ is closed? Let $f : \mathbb R \to \mathbb R$ continuous. Prove that graph $G = \{(x, f(x)) \mid x \in \mathbb R\}$ is closed.  I'm a little confused on how to prove $G$ is closed. I get the general strategy is to show that every arbitrary convergent sequence in $G$ converges to a point in $G$.  Here is what I tried so far:   Let $x_k$ be a sequence which converges to $x$. Since $f$ is continuous, this implies that $f(x_k)$ converges to $f(x)$. At this point, can you say every $(x_k, f(x_k))$ converges to a $(x, f(x))$, so $G$ is closed? Give the "some of your recent flags have been declined" banner some room The "some of your recent flags have been declined" message recently got a banner, which makes it stand out  more (which is nice) but it touches the 'Flag' button, which is less nice. Can it have some margin at the bottom (and perhaps less padding?)    Tested in the latest Safari and Firefox on macOS Catalina. How does the Doctor know how old he is? I've often wondered, how does the Doctor know how old he is? He not only travels through time, but also through space, and visits planets where days can be shorter or longer than 24 hours. How does he 'keep score'?  Also, does he count his age in Earth years or Gallifrey years? They might be completely different in length. I'm trying to change sign text color in Java Edition on Windows 10. According to , this is done using the § symbol:  To enter &quot;§&quot; on Windows with most US/UK English keyboards type ALT + NUMPAD_2 NUMPAD_1  This works for me inside Notepad or this browser. However, when I enter this sequence in the sign input dialog, nothing happens. What could be causing this? Render just part of a final image from Cycles? Formula for the $n$th term of $1, 2, 2, 3, 3, 3, 4, 4 ,4, 4, 5, ...$