I am looking to understand the intuition behind moments of random variables.  I understand the first moment relating to the mean and the second one relating to the variance. But what use does the n-th moment have?   Thank you
While I understand the intuition behind expectation, I don't really understand the meaning of variance and moment.   What is a good way to think of those two terms?
"In" and "on": How can I decide which one to use for vehicles? Examples:   In a car, van, etc. On a bus, boat, motorcycle, etc.   How can one decide which preposition to use? Is memorization the only way or is there a better way?  Note: People generally explain this by either distinguishing between open and closed vehicles or between large and small vehicles. However, the examples I've given defeat both explanations. If $X, Y$ are jointly standard normal with correlation $r$, and $a, b$ are constants, what is $p(Y < b | X < a)$? The application here is interpreting the correlation coefficient $r$ in terms of $X$'s ability to predict $Y$ for extreme values of $X$. For example, if $r = .8$, then what is $p(Y &lt; 0 | X &lt; -2)$? Generating correlated binomial random variables I was wondering if it might be possible to generate correlated random binomial variables following a linear transformation approach?  Below, I tried something simple in R and it produces some correlation. But I was wondering if there is a principled way to do this?  X1 = rbinom(1e4, 6, .5) ; X2 = rbinom(1e4, 6, .5) ;  X3 = rbinom(1e4, 6, .5) ; a = .5  Y1 = X1 + (a*X2) ; Y2 = X2 + (a*X3) ## Y1 and Y2 are supposed to be correlated  cor(Y1, Y2) I would like the user to have full rights on this folder (as well as all sub-directories and files in it):  ~/.blabla   currently owned by root.  I have found numerous posts (in this forum and elsewhere) on how to do this for files but I can't find a way to do it for whole folders. Use of a semicolon before and comma after "however" Several years ago, a previous boss told me to use a semicolon and comma with the word "however".  I've always questioned this and would like to know if the following random sentences are using the correct method.        Our plane was delayed overnight; however, the airlines reimbursed us for lodging.   It looks as though he's upset; however, she told me he always has that look on his face.   I want to find him a nice gift; however, I am a broke until payday.      Normally I would use a less "wordy" sentence in casual writing, but hopefully the example will suffice.  For example, on number 3 I would usually type:      I want to get him a nice gift, but I'm broke until payday. What package should I use to typeset units? I know there are a few packages related to typesetting units:   unitsdef units, which can be seen as a "base package" used by unitsdef SIunits siunitx, which is the successor to SIunits maybe others? like cjwunits and hepunits   What is the difference between them? Do they also work inside Math mode? And, more importantly, which one should I use?  Suggestion for people trying to answer this question: show some examples of how to typeset both simple and complex units. For instance, try typesetting these items:   100 Celsius 3 x 10^5 km/s gravitational constant is measured in N m^2/kg^2 10 kHz = 1 s^{-4} sin(x) meters   I think these examples cover most needs when writing scientific texts: simple measurements (value + simple unit), values written in scientific notation, simple fractional units, complex fractional and squared units, units without any value accompanying them, units with arbitrary exponents, and arbitrary math code instead of a simple value. Should an off-topic question always be downvoted? The upvote tooltip says:      This question shows research effort; it is useful and clear.   The downvote tooltip says:      This question does not show any research effort; it is unclear or not useful.   Sometimes, a question can show research effort, be useful, be clear, but just not in the good place. Voting to close the question and downvoting seems like a double penalty.  Should an off-topic question always be downvoted ? How to prove that orthochronous Lorentz transformations $O^+(1,3)$ form a group? Orthochronous Lorentz transform are Lorentz transforms that satisfy the conditions (sign convention of Minkowskian metric $+---$) $$ \Lambda^0{}_0 \geq +1.$$ How to prove they form a subgroup of Lorentz group? All books I read only give this result, but no derivation.  Why is this condition $ \Lambda^0{}_0 \geq +1$ enough for a Lorentz transform to be orthochronous?  The temporal component of a transformed vector is  $$x'^0=\Lambda^0{}_0 x^0+\Lambda^0{}_1 x^1+\Lambda^0{}_2 x^2+\Lambda^0{}_3 x^3,$$ the positivity of $\Lambda^0{}_0$ alone does not seem at first glance sufficient for the preservation of the sign of temporal component.  And how to prove that all Lorentz transform satisfying such simple conditions can be generated from $J_i,\ K_i$?    For those who think that closure and invertibility are obvious, keep in mind that $$\left(\bar{\Lambda}\Lambda \right)^0{}_0\neq \bar{\Lambda}^0{}_0\Lambda^0{}_0,$$ but instead $$\left(\bar{\Lambda}\Lambda \right)^0{}_0= \bar{\Lambda}^0{}_0\Lambda^0{}_0+\bar{\Lambda}^0{}_1\Lambda^1{}_0+\bar{\Lambda}^0{}_2\Lambda^2{}_0+\bar{\Lambda}^0{}_3\Lambda^3{}_0.$$  And I'm looking for a rigorous proof, not physical "intuition". I read this story in the early 2000s, but it was a Chinese translation so the English version could be older.  The beginning is a bit like the Passengers movie: on a spaceship, a man woke up from stasis too early and found that he could not go back to sleep. So he has to spend his whole life on the spaceship, alone.  For some reason (technical or ethical), instead of waking other people up, he created a fantasy adventure story featuring a brave prince as a pastime. He did stories, and drawings all over the inside of the ship. Then he died, not knowing how people are going to respond to his work. I have got hundreds images of products with clear white backgrounds. I would like to change the white background color to become transparent.   Is there a means of batch processing this particular process with Photoshop or any other applications? Restore Missing "Settings" (gnome-control-center) Icon in Ubuntu 18.04 I have been running Ubuntu 18.04 for a couple of weeks. I upgraded from 16.04 and all went smoothly.   I am not sure what I changed, but this morning I noticed that the "Settings" Icon that launches gnome-control-center is missing from "Show Applications" and the applications menu as well. When I searched from "Show Applications" for gnome-control-center or just settings, nothing showed up.   So, I figured I must have accidentally removed it and figured a reinstall of the package would resolve the issue. I have searched and found several postings where this worked. I tried:  sudo apt install gnome-control-center   And then rebooted - which reinstalled the gnome-control-center and I could then launch it from the command line. However, there was still no Settings Icon in any of the menus.   I also tried many other suggestions including:  sudo apt-get install --reinstall gnome-control-center sudo apt-get install ubuntu-desktop sudo apt install ubuntu-desktop --reinstall sudo apt-get install unity-control-center   However, none of these has been successful in restoring the icon into "Show Applications" or any applications menu.   Anyone have any suggestions on something I haven't tried? Would be much appreciated.  Or, is there a way to just manually recreate the icon?   Output of locate gnome-control-center.desktop:  /usr/share/applications/gnome-control-center.desktop  /home/dccrens/.local/share/applications/gnome-control-center.desktop /home/dccrens/.gnome/apps/gnome-control-center.desktop   I am running Ubuntu 18.04 desktop on kernel 4.15.0-45-generic. Is it possible to use `find -exec sh -c` safely? I'm trying to use find to echo 0 into some files, but apparently this only works with sh -c:  find /proc/sys/net/ipv6 -name accept_ra -exec sh -c 'echo 0 &gt; {}' \;   But using sh -c with find -exec makes me feel very uneasy because I suspect quoting problems. I fiddled a bit with it and apparently my suspicions were justified:   My test setup:  martin@dogmeat ~ % cd findtest  martin@dogmeat ~/findtest % echo one &gt; file\ with\ spaces martin@dogmeat ~/findtest % echo two &gt; file\ with\ \'single\ quotes\' martin@dogmeat ~/findtest % echo three &gt; file\ with\ \"double\ quotes\" martin@dogmeat ~/findtest % ll insgesamt 12K -rw-rw-r-- 1 martin martin 6 Sep 17 12:01 file with "double quotes" -rw-rw-r-- 1 martin martin 4 Sep 17 12:01 file with 'single quotes' -rw-rw-r-- 1 martin martin 4 Sep 17 12:01 file with spaces  Using find -exec without sh -c seems to work without problems - no quoting necessary here:  martin@dogmeat ~ % find findtest -type f -exec cat {} \; one two three  But when I'm using sh -c {} seems to require some kind of quoting:  martin@dogmeat ~ % LANG=C find findtest -type f -exec sh -c 'cat {}' \; cat: findtest/file: No such file or directory cat: with: No such file or directory cat: spaces: No such file or directory cat: findtest/file: No such file or directory cat: with: No such file or directory cat: single quotes: No such file or directory cat: findtest/file: No such file or directory cat: with: No such file or directory cat: double quotes: No such file or directory  Double quotes work as long as no file name contains double quotes:  martin@dogmeat ~ % LANG=C find findtest -type f -exec sh -c 'cat "{}"' \; one two cat: findtest/file with double: No such file or directory cat: quotes: No such file or directory  Single quotes work as long as no file name contains single quotes:  martin@dogmeat ~ % LANG=C find findtest -type f -exec sh -c "cat '{}'" \; one cat: findtest/file with single: No such file or directory cat: quotes: No such file or directory three    I haven't found a solution that works in all cases. Is there something I'm overlooking, or is using sh -c in find -exec inherently unsafe? $f(z)=\frac{z}{1+|z|} $ Is 1-1? Methane’s absorption bands are centered at 3.2 and 7.2 microns -- far off the peak of the Planck spectrum for a 290 K blackbody near 16 microns.  Moreover, its absorption bands overlap with the water absorption region.  So why is methane considered a stronger greenhouse gas than carbon dioxide, which has an absorption band at 15 microns? When trying to restore a backup to a SQL Server Express 2008 database I got the following error:  Restore failed for Server '...\SQLEXPRESS'.  (Microsoft.SqlServer.SmoExtended) System.Data.SqlClient.SqlError: The database was backed up on a server running version 10.50.1600.  That version is incompatible with this server, which is running version 10.00.2531.  Either restore the database on a server that supports the backup, or use a backup  that is compatible with this server. (Microsoft.SqlServer.Smo)   Is there a way to get a backup which is compatible with the older (in my case 10.00.2531) version from the newer (in my case 10.50.1600) version of SQL Server Express? Ubuntu Software doesn't open in Ubuntu 20.04 If i click on Ubuntu Software, it doesn't open. I have a fresh install of Ubuntu 20.04. I tried try to upgrade all packages, but it doesn't fix this problem.  If I try to run killall software-center there is no process with this name, and software-center returns command not found. If I try to reinstall it with apt I have these results:  $ sudo apt-get --purge --reinstall install software-center Reading package lists... Done Building dependency tree        Reading state information... Done Package oracle-java8-installer is not available, but is referred to by another package. This may mean that the package is missing, has been obsoleted, or is only available from another source E: Package 'software-center' has no installation candidate I've heard that i can travel to the US any time before my tourist visa expiry.  Is that true?  (please advise) Can I possibly recover the Windows system partition that I deleted (100MB)? After moving to SSD I deleted the System Partition (100MB) from my previous drive, causing mass destruction.  I tried to delete the System Partition which windows 7 creates (on my previous disc as I moved to SSD) and when I tried to extend the main partition size to include the new Unallocated Space it asked me if I wanted to convert the disc to Dynamic.  I simply pressed yes and the partition simply disappeared into unallocated space. All of my family pictures / videos lost.  After reading an article on Microsoft they said to recreate the partition with the same exact size, so I tried to do that but it didn't work. I did not format the drive at all when I created partitions.  How can I possibly recover the partitions?  Thanks! What does the |= operator do in Java? All nilpotent $2 \times 2$ matrices satisfy $A^{2}=0$