Suppose $X,Y\sim U(0,1)$ are iid random variables and $Z=\min(X,Y)$. Find the pdf and expected value of $Z$.   I've worked this out before when $Z=\max(X,Y)$, but I can't even start here with the maximum replaced with the minimum. Any help?
Problem: Let $X$ and $Y$ be independent and suppose that each has a $\text{Uniform}(0,1)$ distribution. Let $Z = \min\{X, Y\}$. Find the density $f_Z(z)$ for $Z$. Hint: It might be easier to first find $\mathbb{P}(Z &gt; z)$.  Attempted Solution:  Given that $X, Y \sim \text{Uniform}(0,1)$, how do we not just have the following?  $$ f_Z(t) = f_X(t) = f_Y(t) = \begin{cases} 1 &amp; \text{if } 0 \le t \le 1 \\                                           0 &amp; \text{otherwise}                             \end{cases} $$  Of course I'm highly suspicious of this answer because it's not making use of the fact that $X$ and $Y$ are independent, nor is it making use of the provided hint.
I imported the coordinates from an Excel table. They show as single points as intended. Now I want to add columns to the attribute table, but I'm not able to edit it. I wanted to import the following columns from Excel as well, but that doesn't seem to work either.  Sorry for the noob-question, but I couldn't find anything relating the theme through google and such.  Ok, with pictures then: I want to use that to add columns with information to these       You see, the small pensil thingy is greyed out, so I can't edit anything in this layer and I can't add any information to my points.  If I try Ale suggestion I get this error: Requesting raw data from previously published research Defaulting to the sign-up form? Recently I've noticed more and more sign-in / sign-up workflows defaulting to the sign-up option first and providing a minimal "Sign-In / Login" action somewhere else on the page. What's the reason behind this practice?  Examples where I've seen this recently: This problem has been seen on mid-2012 MacBook Pros on Mavericks and on late-2014 Retina MacBook Pros on Yosemite.  One day while using iMessage on the Mac, all the contacts turned red and messages failed to send, immediately returning a "not delivered" error. It also reported when trying to resend the messages that the contacts were no longer associated with an iMessage account.  Things that didn't fix this behavior:   Deleting the com.apple.ids.madrid Removing the Apple ID information from my phone, turning off iMessage on both of the devices, and placing my iPhone in airplane mode for several minutes before turning it on logging in again.   Could someone help me figure out how to solve this? I have noticed that some browsers (in particular, Firefox and ) are very zealous in using cached copies of .css and .js files, even between browser sessions. This leads to a problem when you update one of these files, but the user's browser keeps on using the cached copy. What is the most elegant way of forcing the user's browser to reload the file when it has changed? Ideally, the solution would not force the browser to reload the file on every visit to the page.  I have found  and  suggestion to be useful. It turns out there is a term for this: auto-versioning. I have posted a new answer below which is a combination of my original solution and John's suggestion. Another idea that was suggested by SCdF would be to append a bogus query string to the file. (Some Python code, to automatically use the timestamp as a bogus query string, was .) However, there is some discussion as to whether or not the browser would cache a file with a query string. (Remember, we want the browser to cache the file and use it on future visits. We only want it to fetch the file again when it has changed.) Magento: Merge Product Description and Addition Information Tab In 1D why are vectors, such as, e.g., velocity $v$ and acceleration $a$, not written with a vector arrow? In my textbook instantaneous velocity and acceleration are wrote only as $v$ and $a$ in the chapter of One dimensional motion. Instead, in two dimensional motion chapter they are written with the "arrow" symbol upon them, $\vec{v}$ and $\vec{a}$.  Why if they are both vectors they don't have an arrow in that particular chapter? I just can't get it. The relationship of ${\frak m+m=m}$ to AC Getting "'file' is different from the same file on the system" when I attempt to update through synaptic Encountered an error while updating through Synaptic Manager. Subsequent updates gave the error at the bottom of the output. I'm a noob so any help is appreciated.  al@al:~$ sudo apt-get -f upgrade Reading package lists... Done Building dependency tree        Reading state information... Done Correcting dependencies... Done The following NEW packages will be installed:   libjack-jackd2-0:i386 The following packages have been kept back:   linux-headers-generic skype 0 upgraded, 1 newly installed, 0 to remove and 2 not upgraded. Need to get 0 B/202 kB of archives. After this operation, 493 kB of additional disk space will be used. Do you want to continue [Y/n]? y (Reading database ... 310056 files and directories currently installed.) Unpacking libjack-jackd2-0:i386 (from .../libjack-jackd2-0_1.9.8~dfsg.2-1precise1_i386.deb) ... dpkg: error processing /var/cache/apt/archives/libjack-jackd2-0_1.9.8~dfsg.2-1precise1_i386.deb (--unpack):  './usr/share/doc/libjack-jackd2-0/buildinfo.gz' is different from the same file on the system dpkg-deb: error: subprocess paste was killed by signal (Broken pipe) Errors were encountered while processing:  /var/cache/apt/archives/libjack-jackd2-0_1.9.8~dfsg.2-1precise1_i386.deb E: Sub-process /usr/bin/dpkg returned an error code (1) Why is the Java plugin (JRE) disabled in Chrome? Why is the Java plugin (JRE) is disabled in Chrome? It is some security concern?  From official Java website:     Chrome no longer supports NPAPI (technology required for Java applets)   The Java plug-in for web browsers relies on the cross platform plugin architecture NPAPI,   which has been supported by all major web browsers for over a decade.   Google's Chrome version 45 (scheduled for release in September 2015) drops support   for NPAPI,   impacting plugins for Silverlight, Java, Facebook Video   and other similar NPAPI based plugins.   But anyone knows why? How it could be dangerous for Chrome user with latest version of Java JRE installed? How to SEO a Single-Page website I am creating a new website for a client, and I think a single page website / layout will be pretty neat. There is not that much detailed content, it is a company that imports a lot of products from different companies. So it will be a bit of a showcase of the different types of products / equipment you can order. Of the whole catalog only maybe 10 products are actually shown.  Now I have the basic structure with sections and links like:      #home / #products / #equipment / #services / #contact.    Now from what I understand is that Google does not index links containing #, so there will be no problem of duplicate content, everything will be indexed as the frontpage.  Now what I want to optimize is searching. This company is agent of some product in the country, meaning only they have the permission to import and sell that product. This means  that when somebody searches for product x, this website pops up as the first hit.  Now can I make it that they will be automatically brought to the #products part of the website directly from google.  I was thinking of something like having google index the different sections as different pages. Is something like that possible? How do I Deserialize this XML document:  &lt;?xml version="1.0" encoding="utf-8"?&gt; &lt;Cars&gt;   &lt;Car&gt;     &lt;StockNumber&gt;1020&lt;/StockNumber&gt;     &lt;Make&gt;Nissan&lt;/Make&gt;     &lt;Model&gt;Sentra&lt;/Model&gt;   &lt;/Car&gt;   &lt;Car&gt;     &lt;StockNumber&gt;1010&lt;/StockNumber&gt;     &lt;Make&gt;Toyota&lt;/Make&gt;     &lt;Model&gt;Corolla&lt;/Model&gt;   &lt;/Car&gt;   &lt;Car&gt;     &lt;StockNumber&gt;1111&lt;/StockNumber&gt;     &lt;Make&gt;Honda&lt;/Make&gt;     &lt;Model&gt;Accord&lt;/Model&gt;   &lt;/Car&gt; &lt;/Cars&gt;   I have this:  [Serializable()] public class Car {     [System.Xml.Serialization.XmlElementAttribute("StockNumber")]     public string StockNumber{ get; set; }      [System.Xml.Serialization.XmlElementAttribute("Make")]     public string Make{ get; set; }      [System.Xml.Serialization.XmlElementAttribute("Model")]     public string Model{ get; set; } }   .  [System.Xml.Serialization.XmlRootAttribute("Cars", Namespace = "", IsNullable = false)] public class Cars {     [XmlArrayItem(typeof(Car))]     public Car[] Car { get; set; }  }   .  public class CarSerializer {     public Cars Deserialize()     {         Cars[] cars = null;         string path = HttpContext.Current.ApplicationInstance.Server.MapPath("~/App_Data/") + "cars.xml";          XmlSerializer serializer = new XmlSerializer(typeof(Cars[]));          StreamReader reader = new StreamReader(path);         reader.ReadToEnd();         cars = (Cars[])serializer.Deserialize(reader);         reader.Close();          return cars;     } }   that don't seem to work :-( How does one write on the outside of a circle?  I am looking for sample files/packages which imitate a magazine lay-out. Specifically a page with two columns having a circular picture between the two columns.    Example of the desired layout, created using Word: My GNU/Linux system (Arch) now has libncurses.so.6 rather than libncurses.so.5. But I have upstream's vanilla TeX Live (fully updated) and xindy wants libncurses.so.5:    xindy --version   produces the following error  xindy release: 2.5.1 xindy script version: 1.18 /usr/local/texlive/bin/xindy.run: error while loading shared libraries: libncurses.so.5: cannot open shared object file: No such file or directory   And ldd can confirm the problem:  ldd /usr/local/texlive/bin/xindy.run    gives      linux-vdso.so.1 (0x00007ffc07997000)     libm.so.6 =&gt; /usr/lib/libm.so.6 (0x00007fab4d1b1000)     libcrypt.so.1 =&gt; /usr/lib/libcrypt.so.1 (0x00007fab4cf79000)     libncurses.so.5 =&gt; not found     libdl.so.2 =&gt; /usr/lib/libdl.so.2 (0x00007fab4cd75000)     libc.so.6 =&gt; /usr/lib/libc.so.6 (0x00007fab4c9d1000)     /lib64/ld-linux-x86-64.so.2 (0x00007fab4d4af000)   How can I use xindy without changing my operating system, while using vanilla TeX Live?  2 strategies have occurred to me:   compile xindy from sources against libncurses.so.6; compile and install libncurses.so.5 alongside libncurses.so.6.   Option (2) can be dodgy or can be fine, depending on the details. My suspicion is it may be dodgy for this library, simply because no packages are available for the old version of the library, which might mean there are problems having both installed. Moreover, since everything else is compiled against the new version, I'm not sure whether this would be enough for xindy anyway.  Option (1) I have no idea about. I don't know if this is even vaguely doable or, in fact, where the sources are or what might be required to compile them. (I don't suppose there's any chance a pre-compiled binary is available somewhere? But that is probably hoping for too much ;).)  What is the most practicable approach? This prints 83  System.out.println(0123)   However this prints 123  System.out.println(123)   Why does it work that way? Should I postpone my trip to Paris in 2nd week of Jan in light of recent protests? I’ve a date and I really waited long to make this happen. My gifrfriend is a bit worried about the security issue in Paris. Which locals think that the media is exagerrating the issue and the issue is small and non-threatening for tourists? XeTeX: What happened to \mathcal and \mathscr? Recently I switched from pdflatex to xelatex to be able to use OpenType fonts. I like to use variables highlighted using \mathcal for specific variables, while I used to use \mathscr-typeset variables for matrices. But when I compile with XeLaTeX they look exaclty the same.  Old code  \documentclass{standalone} \usepackage{mathrsfs} \begin{document} $\mathcal{C} = \mathscr{C}$ \end{document}   Output        New code  \documentclass{standalone} \usepackage{unicode-math} \begin{document} $\mathcal{C} = \mathscr{C}$ \end{document}   Output        Broken code  I tried to get back the glyphs from mathrsfs, but it failed this way.  \documentclass{standalone} \usepackage{unicode-math} \usepackage{mathrsfs} \begin{document} $\mathcal{C} = \mathscr{C}$ \end{document}   Output        Question: How can I get back the behaviour? In principle I'd like to have the old \mathcal letters from the pdflatex-version of Computer/Latin Modern.    Alternate solutions (Addendum 2016/05/11) Solving an equation over the reals: $ x^3 + 1 = 2\sqrt[3]{{2x - 1}}$ Solve the following equation over the reals:$$ x^3  + 1 = 2\sqrt[3]{{2x - 1}} $$ I noticed that 1 is a trivial solution, then I tried raising the equation to the 3rd, then dividing the polynomial by $(x-1)$.. But I can't see the solution, how do I go from here? Merge pdfs sequentially I would like to merge 4 pdfs, pdf1.pdf, pdf2.pdf, pdf3.pdf pdf4.pdf together so that the pdfs are spliced, i.e. the first page will be the first page of pdf1, the second the first of pdf2, the third the first of pdf3, etc.  The pdf files are with plain images, no table of contents.  How would I accomplish this? It would be nice to do it from Terminal as well. Are PHP short tags acceptable to use? Here's the information :     There are four different pairs of   opening and closing tags which can be   used in PHP. Two of those, &lt;?php ?&gt;   and &lt;script language="php"&gt; &lt;/script&gt;,   are always available. The other two   are short tags and ASP style tags, and   can be turned on and off from the   php.ini configuration file. As such,   while some people find short tags and   ASP style tags convenient, they are   less portable, and generally not   recommended.   In my experience most servers do have short tags enabled. Typing  &lt;?=   is far more convenient than typing  &lt;?php echo    The programmers convenience is an important factor, so why are they not recommended?