When Building a Character, if a skill proficiency is mentioned twice do i add the proficiency bonus twice?
What happens if I get the same skill from both my background and my class?
I'd like to ask for help with a task that I've been given.  The task goes like this: In a poker game (52 cards), 5 players are given 5 cards each. What is the probability that both the first and the third player will get a full-house?  It's apparent that the probability of the first player getting a full house is  $\frac{\binom{13}{1} * \binom{4}{3} * \binom{12}{1} * \binom{4}{2}}{\binom{52}{5}}$  Then the second player gets 5 random cards, so $\frac{\binom{13}{1} * \binom{4}{3} * \binom{12}{1} * \binom{4}{2}}{\binom{52}{5}} * \binom{47}{5}$  Now the third player is supposed to get a full house, I'm assuming it should look like this: $\frac{\binom{13}{1} * \binom{4}{3} * \binom{12}{1} * \binom{4}{2}}{\binom{52}{5}} * \binom{47}{5} * \frac{\binom{13}{1} * \binom{4}{3} * \binom{12}{1} * \binom{4}{2}}{\binom{42}{5}}$  The fourth and the fifth player both receive 5 random cards, so the final equation should be:$\frac{\binom{13}{1} * \binom{4}{3} * \binom{12}{1} * \binom{4}{2}}{\binom{52}{5}} * \binom{47}{5} * \frac{\binom{13}{1} * \binom{4}{3} * \binom{12}{1} * \binom{4}{2}}{\binom{42}{5}} * \binom{37}{5}* \binom{32}{5}$  This is how I would solve the task, but I'm not sure that my solution for the third player is correct. Could anyone more experienced than me have a look at my solution?  Also I'm sorry if there is a solution for this type of task on this site, I tried looking for it and I found a lot of poker probability questions, most of them were however focused on only one player and not multiple players, which is my case. Problems updating Python from the repositories today (Feb 25, 2021) NOTE: This is a Master Canonical Post for the issues observed on February 25, 2020.  All issues on Feb 25 relating to Python updates not found should be dupe-linked here.  Errors have been seen such as this today, February 25, 2021: Failed to fetch http://security.ubuntu.com/ubuntu/pool/main/p/python2.7/libpython2.7-minimal_2.7.17-1~18.04ubuntu1.3_amd64.deb 404 Not Found  Is there something up with the repositories? Scale Space Between Multiple Objects If I have multiple objects selected can I use scaling to make the objects closer together (without rescaling the objects)? Show that $\frac 1{1+x+y^{-1}}+\frac1{1+y+z^{-1}}+\frac1{1+z+x^{-1}}=1$ if $xyz=1$ If $x.y.z=1$ show that $\dfrac 1{1+x+y^{-1}}+\dfrac1{1+y+z^{-1}}+\dfrac1{1+z+x^{-1}}=1$  My attempt - L.H.S$=\dfrac 1{1+x+y^{-1}}+\dfrac1{1+y+z^{-1}}+\dfrac1{1+z+x^{-1}}$  $=\dfrac y{y+xy+1}+\dfrac z{z+yz+1}+\dfrac x{x+zx+1}$  $=\dfrac{yz}{yz+xyz+z}+\dfrac z{z+yz+1}+\dfrac x{x+zx+1}$  What to do next? Fancyhdr does not apply same header/footer on chapter and non-chapter pages Can it hurt to put my GRE score on my resume? How does CoffeeScript's existential operator work? Is flair tab working correctly? Is the flair tab working correctly?  It is counting aproximately 3 times more points and over 2 times more bronze badges at the time I'm posting it. How can you detect if users have created sock puppet accounts? How many users have created more than one profile on SO to vote themselves on their other original profile? There are some benefits when you have more reputation and sometimes you don't want a single -1 vote on your question or answer. In this case you may have an extra account to convert that -1 vote into 0 vote and  upvote for each of your questions and answers to gain reputation. I think it is not a good thing to do as a good developer.  Is there any way to recognize this situation? I think there should be some stats in each user's profile about how many votes are posted by each user on him/her or something like that.  So how many users have more than one profile? How to handle this situation? I have not created one yet but............ I don't think so :) Draw power from a portable mobile charger to power circuits How can I get to Iceland on a cargo ship? Planning a low budget and environment friendly trip to Iceland from Helsinki, Finland next summer for me and my friend. Haven't been able to find relevant information on possibility for cargo travel (from where - eg. Norway, Denmark? - timetables, prices etc). Expected departure from Helsinki around June 18th, return at latest on July 7th 2015. I'm very thankful for any related advice (and first time on stackexchange, so apologies if I didn't formulate my question in a best possible way) Where does the term $|\psi\rangle\langle\psi|$ come from while calculating the expectation value? Java FileReader encoding issue I tried to use java.io.FileReader to read some text files and convert them into a string, but I found the result is wrongly encoded and not readable at all.  Here's my environment:   Windows 2003, OS encoding: CP1252 Java 5.0   My files are UTF-8 encoded or CP1252 encoded, and some of them (UTF-8 encoded files)  may contain Chinese (non-Latin) characters.  I use the following code to do my work:     private static String readFileAsString(String filePath)     throws java.io.IOException{         StringBuffer fileData = new StringBuffer(1000);         FileReader reader = new FileReader(filePath);         //System.out.println(reader.getEncoding());         BufferedReader reader = new BufferedReader(reader);         char[] buf = new char[1024];         int numRead=0;         while((numRead=reader.read(buf)) != -1){             String readData = String.valueOf(buf, 0, numRead);             fileData.append(readData);             buf = new char[1024];         }         reader.close();         return fileData.toString();     }   The above code doesn't work. I found the FileReader's encoding is CP1252 even if the text is UTF-8 encoded. But the JavaDoc of java.io.FileReader says that:     The constructors of this class assume   that the default character encoding   and the default byte-buffer size are   appropriate.   Does this mean that I am not required to set character encoding by myself if I am using FileReader? But I did get wrongly encoded data currently, what's the correct way to deal with my situtaion? Thanks. Virtualbox not seeing any usb devices in the usb filters settings I was following this question but found a problem.   I used guvcview to test the camera, it works. I installed the 12.04 virtualbox release from their website and installed the extension pack. But when I click the usb with the green plus sign it says no devices available. Which metric to use to evaluate highly imbalance classification model performance I have to do classification model to predict the possibilities of person getting cancer based on certain attributes. The data is highly imbalanced. As per client requirement I have to report model performance based on any one of these 4 metrics AUC_Weighted normalized root mean square log loss Accuracy  Can you suggest me which one should I use? 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Compute $E(X\mid X+Y)$ for independent random variables $X$ and $Y$ with standard exponential distributions Being $X$ and $Y$ independent random variables distributed as $\mathrm{Exponential}(1)$ and let $T=X+Y$ Calculate $E(X|T)$.  This is my attempt at solving this:  Being $Z=\sum_{i=1}^{n}P_{i}$ where $P_{i}$~$\mathrm{Exp}(\lambda)$ then using it's MFG you have that $$M_{P_i}(t)=\frac{\lambda}{\lambda-t}$$ then $$M_{Z}(t)=M_{\sum{P_{i}}}(t)=(M_{P_{1}})...(M_{P_{n}})=(\frac{\lambda}{\lambda-t})^n$$ with this being the MFG of a $\mathrm{Gamma}$ distribution with parameters $(n,\lambda)$  With this result is easy to see that $T$~$\mathrm{Gamma}(2,1)$  Now $E[X|T]=\int xf_{X|T}(x|t)dx$  Then using Bayes' theorem we can make $$f_{X|T}(x|t)=\frac{f_{T|X}(t|x)f_{X}(x)}{f_{T}(t)}$$ then $$f_{T|X}(t|x)=Pr(T=t|X=x)$$ $$=Pr(X+Y=t|X=x)$$ $$=Pr(x+Y=t|X=x)$$ $$=Pr(Y=t-x)=f_{Y}(t-x)$$  Using this result we can now rearrenge $$f_{X|T}(x|t)=\frac{f_{Y}(t-x)f_{X}(x)}{f_{T}(t)}$$ $$=\frac{e^{-(t-x)}.e^{-x}}{\frac{te^{-t}}{\Gamma(2)}}$$ $$=\frac{1}{t}$$ then $$E[X|T]=\int (x)(\frac{1}{t})dx$$  And this where I got stuck because $1_{x\epsilon(0,\infty})$, I made this explanation step-by-step hoping that someone can se easily check where I went wrong. I would aprecciate a step-by-step answer, thanks. My friend recently received a new digital drawing tablet (Wacom Intuos Pro). Among other features, there is a hole that resembles a charm hole found on mobile phones:    Other parts of the package (e.g. pen) do not have such holes, so it isn't possible to attach them using a band. What is the purpose of this hole? Is it just for attaching various charms and such? Is the universe finite or infinite?