Two numbers $x$ and $y$ are randomly and independently selected in the interval $[0,1]$. Find the density and distribution functions of the random variable $X+Y$.  I have doubts about how to approach this exercise, because I do not know if the variables satisfy a uniform distribution, although I have not until the moment very clear the concept of convolution to find what is required. Any contribution would be appreciated, thank you very much!  Not a duplicate. Uniform distribution is not mentioned in the case of this question
I am trying to understand an example from my textbook.  Let's say $Z = X + Y$, where $X$ and $Y$ are independent uniform random variables with range $[0,1]$. Then the PDF is $$f(z) = \begin{cases} z &amp; \text{for $0 &lt; z &lt; 1$} \\ 2-z &amp; \text{for $1 \le z &lt; 2$} \\ 0 &amp; \text{otherwise.} \end{cases}$$  How was this PDF obtained?   Thanks
I have snippets of Html stored in a table. Not entire pages, no  tags or the like, just basic formatting.  I would like to be able to display that Html as text only, no formatting, on a given page (actually just the first 30 - 50 characters but that's the easy bit).  How do I place the "text" within that Html into a string as straight text?  So this piece of code.  &lt;b&gt;Hello World.&lt;/b&gt;&lt;br/&gt;&lt;p&gt;&lt;i&gt;Is there anyone out there?&lt;/i&gt;&lt;p&gt;   Becomes:  Hello World. Is there anyone out there? Someone who just thinks they know what they're talking about The state postulate is as follows: The state of a simple compressible system is completely specified by two independent, intensive properties. My first question is whether there is any justification for this postulate or whether it is simply an empirical law? That is, why is it not the case that 3 intensive variables are required to fix the state or even 4? If it is an empirical law with no justification and just happens to be a law our universe abides by, then why is it not one of the laws of thermodynamics as it clearly provides foundational value to the field of thermodynamics? My second question pertains to how we can know whether 2 intensive variables are in fact independant. Say temperature $T$ and specific volume $v$ for example. If we are given a thermodynamic problem, how would we know whether these are independent or not? or perhaps specific internal energy $u$ and pressure $P$. Are there certain combinations that are simply always independent of each other or does independence between intensive variables vary from problem to problem and require a full understanding of the problem at hand? Let us take a phase change for example. From my understanding of phase changes, I know that the boiling temperature is dependent on the pressure and hence I won't be able to use $T$ and $P$ as 2 variables to completely specify the state. But how would I know know what combinations of intensive variables will be independent in this case or any other case for that matter? Does it simply require rote memorization of all independent pairs of intensive variables for all thermodynamic problems or is there a more simple way to figure out what is independent and what isn't? I hope this question makes some sense and any help would be most appreciated! Homework question on whether two quotient spaces are homeomorphic I'm trying to use scrlayer-scrpage with a twosided document using the scrartcl class but somehow can't manage to format the plain pagestyle in a way that is similar to the scrheadings style. I prepared the following MWE – thanks in advance!  \documentclass[12,a4paper,twoside]{scrartcl} \usepackage[automark,headsepline,footsepline,markcase=nouppercase]{scrlayer-scrpage} \renewcommand*{\sectionmarkformat}{} \renewcommand*{\subsectionmarkformat}{} \renewcommand*{\headfont}{\normalfont} \automark[subsection]{section} \chead{\leftmark} \cfoot{\pagemark} \ihead{} \ohead{} \ifoot{} \ofoot{}  \begin{document}  \pagestyle{scrheadings}  \section{Blah.}  Blah.  \newpage  \section{Blah.}  Blah.  \newpage  \pagestyle{plain.scrheadings}   \section{Blah.}  Blah.  \newpage  \section{Blah.}  Blah.  \end{document} Preferred languages: C/C++, Java, and Ruby.  I am looking for some helpful books/tutorials on how to write your own compiler simply for educational purposes. I am most familiar with C/C++, Java, and Ruby, so I prefer resources that involve one of those three, but any good resource is acceptable. why can't I edit /proc/sys/kernel/perf_event_max_sample_rate with vi I'm root, running Centos8 on bare mental and permissions on /proc/sys/kernel/perf_event_max_sample_rate are as follows  -rw-r--r--. 1 root root 0 Oct  3 14:00 perf_event_max_sample_rate   I want to change the sample rate by opening this file with vi, making the change and then writing it with either w or w!. When I do so it comes back with  perf_event_max_sample_rate" E667: Fsync failed  When I try to quit, it tells me  E37: No write since last change (add ! to override)   So I can't change the value with vi.  However I can change the value with   echo 4000 &gt; /proc/sys/kernel/perf_event_max_sample_rate   Is this simply because /proc is not a real file system and that all changes to things in /proc would have to be made using echo with a redirect, or maybe sed?  Is this behavior documented somewhere? The reason that I ask is because this is happening to LiDAR, and I am inclined to use lidar because it is easier to read. How does some of the black hole (BH) mass escape the event horizon (EH) of either BH, or the merged EH of two merged BHs? Can someone identify the fonts used in the words "nature methods" in the following image?    I think that the word "nature" is in Times or Times New Roman (?) but can't figure out what font the word "methods" is in.  Any ideas? How does a credit card company make any money off of me using their card if there are no fees associated with the card (I don't pay any extra) and I pay off my balance on time every month (so I don't pay any fees ever for this either).  Are they just banking on the fact that many people don't do this and end up owing them money? Function whose inverse is also its derivative? What is the rule for adjective order? I remember being taught that the correct order of adjectives in English was something along the lines of "Opinion-Size-Age-Color-Material-Purpose."  However, it's been a long time and I'm pretty sure I've forgotten a few categories (I think there were eight or nine). Can anyone fill them in? How to fix byte array java.lang.NullPointerException If I've decided to update my SE avatar (in any of the various ways well described in the answer to this ), am I able to return to either the original stock image or previous avatar images I have used? Do the SO admins have any plans to release the underlying code for SO at all? I appreciate that the code may be part of their competitive advantage, but it strikes me that the underlying system would work for any topic, not just programming.  I am not advocating this, just curious really, but figured it might be under consideration as most of the value in SO is in the questions and answers, which have been released under a relatively open CC license. What defines a PC's consciousness of self, memories and knowledge? Forgotten iOS Restrictions Password/Passcode In  (2014) the human race seemed to be facing pretty poor odds until they discovered a convenient wormhole placed by an unknown entity expressed as "they". Later in the movie, we discover that       "they" are actually the human race in the future, reaching back in  time to save itself.   The end of the movie gets a little wild on the physics end, and I'm happy to take that ending as is - no need for it to make sense - but one very basic detail does bother me:  How could the human race have gone back in time to save itself from circumstances that would have caused us to go extinct without our own help (the convenient wormhole)? javascript not working, working on fiddle but not on my webserver