You've got a discrete uniform distribution - what is the expected number of trials until each point is hit at least once?  I started my thinking with maybe a Geometric distribution representing each individual point - if your probability of success is 1/100 in the uniform distribution, then would the number of trials until first success be 100? That is for one point so to have 100 points = 10000 trials until you hit 100 points?? That doesn't sound right, because if you fail to hit one specific point, you've succeeded in hitting a different point, so it's not exactly a matter of first success at one point. What am I missing?  Follow up question: how about after 100 trials, what percentage of points are expected to have been hit?
What is the average number of times it would it take to roll a fair 6-sided die and get all numbers on the die?  The order in which the numbers appear does not matter.  I had this questions explained to me by a professor (not math professor), but it was not clear in the explanation.  We were given the answer $(1-(\frac56)^n)^6 = .5$ or $n = 12.152$  Can someone please explain this to me, possibly with a link to a general topic?
IEEEtran - How to include ORCID in TeX/PDF with PdfLatex This question led to a new package:   I would like to display the ORCID id in an author list in an IEEEtran pdf, like that:  Is there a standard way to include it in an IEEEtran article with PdfLaTeX? I used two approaches from , but I failed. One is to insert the ORCID icon in the author list. I used the blow code: \author{Ali Al-Obaidi \href{https://orcid.org/0000-0000-0000-0000}{\includegraphics[scale=1]{figures/orcid_16x16.png}}}  where orchid_16x16.png is provided in the link . But the result is that the icon is not clear enough, even I replaced it with a different size. The other approach is to use the  package, like that: \usepackage{academicons} \definecolor{orcidlogocol}{HTML}{A6CE39} \author{AAA \href{https://orcid.org/0000-0000-0000-0000}{\textcolor{orcidlogocol}{\aiOrcid}}}  However, the result is like that:  And I also got two errors: &quot;Latex Error: Encoding scheme 'TU' unknown&quot; and &quot;Bad character code (59865)&quot;. In the latest academicons.sty (see ), academicons use the font TU. However, it seems that the compiler PdfLateX cannot support this font. Thus, is there anyone that knows a standard way to include it in an IEEEtran article with PdfLaTeX? Please help me. Can a multiclass character with 1 level of wizard copy any wizard spell they find into their spellbook? The &quot;Your Spellbook&quot; sidebar for the wizard includes the following line:  Copying a Spell into the Book. When you find a wizard spell of 1st level or higher, you can add it to your spellbook if it is of a level for which you have spell slots and if you can spare the time to decipher and copy it.  Does this mean that a Wizard 1/Cleric 19 can copy any wizard spell they find into their spellbook? Is there anything preventing them from casting these spells? From A Classical Introduction to Modern Number Theory by Ireland and Rosen, page 33:     Corollary 1 (Euler's Theorem). If $(a,m) = 1$, then $a^{\phi(m)} \equiv 1\,(m)$.      Proof. The units in $\mathbb{Z}/m\mathbb{Z}$ form a group of order $\phi(m)$. If $(a,m) = 1$, $\bar{a}$ is a unit. Thus $\bar{a}^{\phi(m)} = \bar{1}$ or $a^{\phi(m)} \equiv 1\,(m)$.   If I'm interpreting this correctly, this proof implicitly uses the fact(?) that if $G$ is a group and $x\in G$, then $x^{|G|}=1$, where $1$ is the identity element of $G$.  If this is indeed true, can someone explain why? (I have had no prior exposure to group theory.) How to find the best route through multiple points? I am using postgreSQL, postGIS and pgrouting. Now I am really confused on how am I going to find the shortest path between multiple points.   I know how to find it between two points through dijkstra but I am confused how to accomplish the same result with more than two points.   I have done some research and found this:    But still I did not understand if its the right way and how to install it. Proof of $Y=F_X(X)$ being uniformly distributed on $[0,1]$ for arbitrary continuous $F_X$ Can I use old Minolta AF lenses on my new Canon? I just recently bought my first DSLR, a Canon Rebel t2i/550d. I use it mostly for video and it works wonderfully. I bought the kit lens with it, but I am looking to expand my lens collection. I found a set of old Minolta lenses from my dad, and I was wondering if I could use them on my new camera. The lenses are: a Sigma UC zoom 28-105 f4-5.6, a Minolta Maxxum zoom 70-210mm, a Minolta Maxxum zoom 28-58mm and a Kalimar 500mm lens. I know about the crop factor and that the auto focus won't work, but that does not bother me. Is there an adapter for Minolta AF/Sony to Canon EF mount? Any help is appreciated. Thanks! The plural of "person" is "people".  The plural of "people" is "peoples". Person-people-peoples is the only sequence like this that I know of, but I'm looking for another.  (The equivalent question is, is there another plural noun which has become a singular countable collective noun?)  EDIT  For those of you that think that people is nothing but a collective noun (and not an irregular plural, like mice), I urge you to consider:   Do you treat other collective nouns as plurals?  One person, two people, but one star, two galaxy? Do you treat other plurals as collective nouns?  You can certainly say "a galaxy of stars" but do you say "a mice of mouses"?    For those of you that think the customary plural of person is persons, try it on the next three, uh, persons you see: "Finish this sentence: 'one person, two _ ?' " Derivative of a factorial What is ${\partial\over \partial x_i}(x_i !)$ where $x_i$ is a discrete variable?  Do you consider $(x_i!)=(x_i)(x_i-1)...1$ and do product rule on each term, or something else? Thanks. Illogical GTK theme behaviour on Ubuntu 18.04 how to reset gnome panel? I think my gnome-panel is messed up because I alt+right click it and nothing pops up.  I'm on 12.04, classic gnome desktop.  so I used locate and found gnome-panel in .gconf somewhere, how do I clear just gnome-panel's settings so that I can add things to my panel again?   edit:  matt: ~/.gconf $ find|grep -iw panel ./desktop/ibus/panel ./desktop/ibus/panel/%gconf.xml ./apps/gnome-settings/gnome-panel ./apps/gnome-settings/gnome-panel/%gconf.xml AngularJS leaves comments in HTML: is it possible to remove them? How do I get the next element in HTML using JavaScript?  Suppose I have three &lt;div&gt;s and I get a reference to one in JavaScript code, I want to get which is the next &lt;div&gt; and which is the previous. "Give him a box that everyone knows what it contains."  Is this correct English? It sounds wrong to me. Why is 'ping' unable to resolve a name when 'nslookup' works fine? On my Windows XP workstation, I can find the machine I want to connect to in DNS with nslookup:  nslookup wolfman Server: dns.company.com Address: 192.168.1.38  Name: wolfman.company.com Address: 192.168.1.178   But, when I try to connect to that machine, I get an error telling me that the machine can't be found (i.e., can't be looked up in DNS):  C:\&gt; ping wolfman Ping request could not find host wolfman. Please check the name and try again.   I am able to connect if I use the IP address directly:  C:\&gt; ping 192.168.1.178  Pinging 192.168.1.178 with 32 bytes of data:  Reply from 192.168.1.178: bytes=32 time=41ms TTL=126 Reply from 192.168.1.178: bytes=32 time=41ms TTL=126 Reply from 192.168.1.178: bytes=32 time=44ms TTL=126 Reply from 192.168.1.178: bytes=32 time=38ms TTL=126   I could work around this by adding an entry to my hosts file, but I would rather find out why this is happening.  The problem is transient, most of the day I can connect to the machine just fine.  How is this possible?  ETA: I left this out for brevity, but it was asked for:  C:\&gt; ping wolfman.company.com Ping request could not find host wolfman.company.com. Please check the name and try again.   ETA: Other applications get the same results.  I only tried ping to simplify.  telnet can't connect, Cygwin apps print a "unknown host wolfman" message.  Update: Using wireshark, I found that my workstation is not attempting a DNS lookup.  It's just reporting the "could not find host" error message. How to show that $\mathfrak{sl}_n(\mathbb{R})$ and $\mathfrak{sl}_n(\mathbb{C})$ are simple? Create file and its parent directory I know that touch command creates a file:  touch test1.txt   but how I can create a file and its full path?  for example my desktop contains nothing:  ~/Desktop/$ ls ~/Desktop/$   and I want to create 1.txt in ~/Desktop/a/b/c/d/e/f/g/h/1.txt. Can I do this with a simple command like:  $ touch ~/Desktop/a/b/c/d/e/f/g/h/1.txt   instead of create full path manually and then create the file? :  Not ten minutes ago, I received this error, twice:  And also an &quot;Oops, something bad happened&quot; error.  I'm also getting question posting errors.  Can we fix this, please? Is the empty set a subset of itself? How do I remove "permission denied" printout statements from the find program? Code   find / -name netcdf   Output  find: `/root/.dbus': Permission denied find: `/root/.gconf': Permission denied find: `/root/.gconfd': Permission denied find: `/root/.gnome': Permission denied find: `/root/.gnome2': Permission denied find: `/root/.gnome2_private': Permission denied How do I avoid rendering glitches from overlapping faces?