Players of a certain TRPG have characters with 6 ability scores, each ability score ranging from 3-18. One method of generating those is by rolling 4d6 drop lowest. That means four six-faced-dice are rolled, and the three highest results are added.   What's the probability that, given 5 players, one player will have a highest ability score equal or lower than the lowest ability score of another player?   The related question  shows how to get the distribution of 4d3 drop lowest, but how do I get from there to an answer of my question above?   A good answer would explain the result in a way that a statistics novice can follow.
Repeatedly rolling a six sided die four times and summing the highest three results gives you a distribution with what mean and standard deviation?  I've only taken AP statistics, but I would like to learn how to do this.
Get path to application? How can a user determine the path to an application being showed in launcher?  This is meant for non-programmers or experts, so terminal commands are not really suited for them. Why: we need to make our users able to drag files/folders on our applications, a standard OS feature entirely missing in Ubuntu. This is a canonical question   How do I jailbreak an iPhone or iPad (to install a package manager like Cydia or Sileo for tweaks) on:   iOS/iPadOS 13 iOS 12 iOS 11 iOS 10 iOS 9 iOS 8 Solving the matrix equation $AP=PB$, where $A$ and $B$ are similar Currently I'm stuck with this problem:     The following matrices are similar to each other.      $$A=\begin{bmatrix}-3&amp;0\\8&amp;4\end{bmatrix},\qquad B=\begin{bmatrix}-4&amp;4\\-2&amp;5\end{bmatrix},\qquad C=\begin{bmatrix}k&amp;1\\m&amp;-2\end{bmatrix}.$$      How do you find the matrix $P$ such that $AP = PB$?       And how can you calculate the values of $k$ and $m$?      Thank you in advance. What do you call someone who always puts blame on others? jQuery get the rendered height of an element? iBooks library like effect How do I deal with "unauthenticated sources" errors in the Software Center? Bad Eyesight and Evolution Why do many humans have bad eyesight, such as near-sightedness, which hampers performance in a wide variety of tasks? Shouldn't there be evolutionary pressure towards better eyesight? What WordPress API function lists active/inactive plugins? Find asymptotic of recurrence sequence Given a sequence $x_1=\frac{1}{2}$, $x_{n+1}=x_n-x_n^2$. It's easy to see that it limits to $0$.  The question is: is there exists an $\alpha$ such, that $\lim\limits_{n\to\infty}n^\alpha x_n\neq0$.  I tried to find explicit formula for $x_n$, but did not succeed. I stucked at that point: if $a_1=(\frac{1}{4})^2$, $a_n=(a_{n-1}+\frac{1}{4})^2$, then $x_n=-a_{n-2}+\frac{1}{4}$ for $n\ge3$.   Thanks for any ideas and help. How precise must the energies match for absorption of photons? According to Quantum Mechanics, in order for an atom to absorb a photon the energy of the photon must be precisely that of a "jump" between energy states of the atom.  How precise must it be?   If I create a photon with an energy within an error of 0.0001% of that of an energy state, will it be absorbed by my atom? How To Program A Bash Script That Presses A Certain Combination Of Keys? Please, i need someone to help me in making a very simple bash script. The job of this script is just to press a certain combination of keys on the keyboard.  My objective is to create a script that would turn off the Kubuntu desktop effects completely. The key combination for that is: "Left-ALT + Left-Shift + F12". I am aware that there is a widget that might do this job, but i am trying to learn how to accomplish it with a bash script.  I have tried to do an online search but i guess i was choosing the wrong set of keywords. I did not manage to reach a tutorial or a reference that would mention this task.  Thanks in advance for your help!  P.S: Any suggestions, references, notes, comments or tutorials would also be greatly be appreciated. Clock shows wrong time after switching from Ubuntu to Windows 10 I have dual booted Windows 10 and Ubuntu 16.04 in UEFI mode (secure boot off). My time in BIOS is correct.  When I boot into Ubuntu and then boot into Windows 10, it shows the wrong time. I have to correct it manually or by the internet in Windows 10, and when I reboot into Windows 10 then it is not a problem. The clock will show the correct time. And then when I reboot to Linux the clock is correct, but switching back to Windows 10 the clock messes up again. Multiplying by a $1\times 1$ matrix? For matrix multiplication to work, you have to multiply an $m \times n$ matrix by an $n \times p$ matrix, so we have $$\bigg(m \times n\bigg)\bigg(   n\times p \bigg).$$  But what about a $1 \times 1$ matrix? Is this just a scalar? But every matrix can be mulitplied by a scalar; so do $1 \times 1$ matrices break the rule? $\mathbb{F}_p[X]/(X^2+X+1)$ is a field iff $p \equiv 2 \bmod 3$ One of is followed by plural noun/pronoun and singular helping verb Legal issues around using real players names and team emblems in an open source game QR Codes generation from MySQL rows Hi currently Nagios sends notifications from nagios@server.domain.com, How do I go about configuring this? Thanks I'm trying to prove that  $$ \left| \frac{1}{x}-\frac{1}{y} \right| $$  is a metric on $X = \mathbb R^+$.  The properties of non-negativity and symmetry are obvious (do I actually even need to prove them?), but the tricky one is, as usual the inequality property, i.e.  $$ d(x,z) \le d(x,y) + d(y,z) \text{ for any } z \in X. $$  So, ok, I have that  $$ d(x,z) \le d(x,y) + d(y,z) \\ \iff \left| \frac{1}{x}-\frac{1}{z} \right| \le \left|\frac{1}{x} - \frac{1}{y} \right| + \left|\frac{1}{y} - \frac{1}{z} \right| \\ \iff \left| \frac{1}{x} \right|- \left| \frac{1}{z} \right| \le \left| \frac{1}{x}-\frac{1}{z} \right| \le \left|\frac{1}{x} - \frac{1}{y} \right| + \left|\frac{1}{y} - \frac{1}{z} \right| $$  ...and that's about as far as I've gotten–which is to say, not very far. I also tried multiplying both sides by $ \left| \frac{1}{x}-\frac{1}{z} \right| $, but that wasn't very fruitful. If someone could point me in the right direction, it'd be greatly appreciated. Thanks.