What is the probability hat two particular players verse in Wimbledon if it begins with $16$ players?
In a tennis tournement of 128 players, elimination system, what is the probability that two twins will meet at some point?
I'm in UV Editor and trying to snap the 2d cursor to the vertex ( while the vertices are visible). I turn ON snap and set it to 'vertex mode' , but the 2d cursor won't snap to any visible vertex at all. I can only make it snap to the grid (increment node). Is it a bug ? or did i miss something here ? i'm using 2.8. Where is the operator panel in Blender 2.8? Previous posts                  As of today, the Moderator Flag Dashboard is officially graduated and the old version sent to the smelter's yard.  Based on stats from the past month, virtually all moderators were already on the new UI (thank you) so you hopefully won't notice any change.  That said, I would like to highlight the handful of improvements we made over the last month and a half based on your feedback:   A more responsive navigation bar at the top of moderator pages, improving the mobile experience. Similarly, , increasing room on the screen for the first question. . .  Not only do the headers look better, they now function better.  Now you scroll to and highlight the post/comment each time you click the link, not just the first time. .  Posts by the same user are grouped together and ordered newest first. .  We eliminated the VLQ (auto) side effect so now "Resolve all flags (auto)" doesn't do anything surprising.  If you still want to leave a comment or decline, you can do so with the buttons next to the individual flags.   Bugs and Feature Requests  Since this project is officially launched, all bugs and feature requests should be done in the form of questions tagged  on MSE, not answers on this post.  Feel free to post an answer here if you have specific concerns about the release process. I need to find my external IP address from a shell script. At the moment I use this function:   myip () {      lwp-request -o text checkip.dyndns.org | awk '{ print $NF }' }   But it depends on perl-libwww, perl-html-format, perl-html-tree installed. What other ways can I get my external IP? Prove that $\sqrt[n]{n!}$ is increasing and diverges I have to prove that $a_n$ is (strictly) increasing and diverges  $a_n = \sqrt[n]{n!}$ ;  n $\in$  $\ \mathbb{N}$  From sequence I see that $a_n$ increasing to infinitive.  $\sqrt[1]{1!}=1 ,\  \sqrt[2]{2!} \approx 1.41, \  \sqrt[3]{3!}  \approx 1.81 ,...,  \sqrt[n]{n!} $ This is a basic question on Box-Jenkins MA models. As I understand, an MA model is basically a linear regression of time-series values $Y$ against previous error terms $e_t,..., e_{t-n}$. That is, the observation $Y$ is first regressed against its previous values $Y_{t-1}, ..., Y_{t-n}$ and then one or more $Y - \hat{Y}$ values are used as the error terms for the MA model.  But how are the error terms calculated in an ARIMA(0, 0, 2) model? If the MA model is used without an autoregressive part and thus no estimated value, how can I possibly have an error term? Is it correct to say e.g. "I like your way of wearing" or "the way you wear looks perfect"?  Is it politely? Is it in use or not? May I use "the way you wear" referring to whole wearings including dress, scarf, hat, bracelet. jewellery, etc?  Thank you for your suggestions in advance. To give you some background, I have a grasp on the basics of statistics and probability theory and even remember touching Bayes theorem at the university data mining course. But being a few years away from the university made my math got extremely rusty (so much for last-minute pre-exam cramming). While I remember various random basic concepts, there are a lot of gaps in my understanding of them.  What would be a good material (a book, a site, or otherwise equally accessible medium) to revise the fundamentals and go beyond basics? I'd like a book that can be actually read as a book (most statistics books are really dry and are close to being reference material, rather than a book). Proof of $1+x\leq e^x$ for all x? when EditText is empty and click calculateButton, app crashes With the Taylor series representation of $\sin$ or $\cos$ as a starting point (and assuming no other knowledge about those functions), how can one:  a. prove they are periodic?  b. find the value of the period? Windows 7 SP1 Windows Update stuck checking for updates Number of factors of a big number How to find the number of factors of $884466000$ without using a calculator? Detection of the Electric Charge of a Black Hole Can I visit Chicago during a 5.5 hour layover in O'Hare? I am getting error:     The argument 2 of the "JSON_VALUE or JSON_QUERY" must be a string literal   ...while trying to pass variable as parameter to JSON_QUERY function. Please help me to resolve it.  DECLARE @cnt INT = 1; DECLARE @cnt_total INT = 1; DECLARE @json NVARCHAR(MAX); DECLARE @json1 NVARCHAR(MAX); declare @str  VARCHAR(200);  WHILE @cnt &lt;= 10 BEGIN     set @str = '$.Seasons[0].Products['+convert(varchar,@cnt)+'].ProductChannels';     set @str = char(39) +@str+ char(39);     PRINT @STR     select @json = json_query(jfile,@STR) from Import.tstjson; --MORE CODE         SET @cnt = @cnt + 1; END   Sample data:  {   "Seasons": [     {       "Season": "12321231",       "Products": [         {           "ProductId": "211",           "ProductChannels": [             {               "ChannelId": 1,               "WeekQuantities": []             }           ],           "ccc": 3,           "Tttt": 4         }       ]     }   ] } Problem 20-9 in Lee's Introduction to Smooth Manifolds (2nd Ed.) asks to prove that for a Lie group $G$, and for $X, Y\in \text{Lie}(G)=\mathfrak g$, there is $\epsilon&gt;0$ and a smooth map $Z:(-\epsilon, \epsilon)\to \mathfrak g$ such that   $$(\exp tX)(\exp tY) = \exp\left(t(X+Y) + \frac{1}{2}t^2[X, Y] + t^3 Z(t)\right)$$   What we want to show is that the first and second term in the Taylor expansion of $\exp^{-1}\left((\exp tX)(\exp tY)\right)$ are $t(X+Y)$ and $\frac{1}{2}t^2[X, Y]$ respectively.  Calculating the first term is easy since we just need to differentiate $\exp^{-1}((\exp tX)(\exp tY))$ with respect to $t$ at $t=0$ once, and this gives the desired result.  But for the second term we need to take the second derivative at which I am stuck. My fiancée and I are looking for a good Caribbean cruise in October and were wondering which islands are best to see and which Cruise line to take?  It seems like a lot of the cruises don't run in this month due to Hurricane season so I'm looking for other good options.  EDIT We'll be travelling in 2012. Find the probability that a geometric random variable $X$ is an even number Who can use magic scrolls? I'm confused about who can use scrolls in 5e. In the DMG, p139 under Magic Item Categories: Scrolls, it states that:     Any creature that can understand a written language can read the   arcane script on a scroll and attempt to activate it.   This implies that anyone can try to cast a spell using a scroll. However, on p.200 in the Spell Scroll entry it states that:     If the spell is on your class's spell list, you can use an action to read the scroll and cast its spell without having to provide any of the spell's components. Otherwise, the scroll is unintelligible.   Then there is the bit about a DC 10 + scroll spell level ability check if the spell is higher than a spell slot that you can cast.     If the spell is on your class's spell list but of a higher level than you can normally cast, you must make an ability check using your spellcasting ability to determine whether you cast it successfully. The DC equals 10 + spell's level. On a failed check, the spell disappears from the scroll with no other effect.    So, which is it? Can anyone who can read a language use a scroll (like a fighter) if they make an arcana check, or just a PC with that specific spell in their spell list (only spell casters)?