I am confused at how the normal distribution's PDF capable of calculating a density for a single variable. I understand that the CDF probability of an exact continuous random variable $X$ is 0. Therefore, to calculate probability of $X$, we may define a range such that  probability of $X$ is $P(a &lt; X &lt; b)$. It appears this range is usually referred to as the interval (please correct me if I am wrong).  PDF for normal distribution is $\frac{1}{\sigma\sqrt{2\pi}}\, e^{-\frac{(x - \mu)^2}{2 \sigma^2}}$ so if we assume $x=1$, $\mu=0$ and $\sigma=1$ the result from these parameters is 0.2419707 density using dnorm in R. How is the PDF capable of coming to this conclusion as we do not specify a interval?
On the , there is this line:      $p(\mathrm{height}|\mathrm{male}) = 1.5789$ (A probability distribution over 1 is OK. It is the area under the bell curve that is equal to 1.)    How can a value $&gt;1$ be OK? I thought all probability values were expressed in the range $0 \leq p \leq 1$. Furthermore, given that it is possible to have such a value, how is that value obtained in the example shown on the page?
I have a directory full of images:  image0001.png image0002.png image0003.png ...   And I would like a one-liner to rename them to (say).  0001.png 0002.png 0003.png ...   How do I do this? Magic leaves "smudges" and a sorceress becomes a book I could use some help identifying a book I read some time in the last year or so. The book goes between two different stories:  1) A student of magic finds a book in a cave that turns out to be a person transformed into a book. The book talks to the student and they share thoughts. At some point, the student runs away, chase ensues, and at the very end of the book, he manages to travel to another plane.  2) A girl in a religious society where magic is forbidden. She is the daughter of painters. She discovers she can see magic. Falls in love with some random painter, risks performing magic to not be pregnant, does it again so she can, and is arrested and sent to some prison thing.  The common element between the stories is that magic use leaves behind a smudge of some kind that can be visible.  Any assistance is appreciated. Get the title instead of the number of a referenced chapter/section? can't get placeholder attribute to work in IE using iframe I want to clear all previous commands from the history of my server. I used history -c and it seems all things are cleared but when I ssh to the server, all the commands are still there.  How can I clear them permanently? Help for Mathematics High school I'm looking for mathematics books, courses + exercises for high school level. My daughter was high school certificated but she has stopped her studies for 5 years. She would like to be involved in new educational program but she needs to restore her mathematic capabilities.  Could you help me to identify which mathematics books can help her?  Thanks a lot for your reply,  FR. Switching languages in bibliography with biblatex I would like to have a bibliography with both Cyrillic and Latin and the main document language being English. How can I make biblatex to automatically switch between languages? (without using XeTeX as suggested by some) The minimal example returns an error if the main language is English. However, with the main language being Russian the document works.  \documentclass{article}  \usepackage[utf8]{inputenc} \usepackage[russian,english]{babel}  \usepackage[backend = biber,babel=other]{biblatex} \usepackage{csquotes} \addbibresource{library.bib}  \begin{document} %\selectlanguage{russian} %if the main document language is Russian the bibliography is compiled without any problem. This is a test. \parencite{Bara2006,Baranov2001}  \printbibliography  \end{document}   The .bib entries are  @book{Bara2006, address = {New York}, author = {Bara, Judith}, publisher = {Routledge}, title = {{English Citation entry}}, year = {2006} }  @book{Baranov2001, address = {Санкт-Петербугр}, author = {Баранов, Николай А}, title = {{Эволюция взглядов}}, year = {2001} } Passing data between view controllers Why is the change in Hamiltonian for an active infinitesimal canonical transformation defined the way it is? I'm trying to understand infinitesimal canonical transformations and conservation theorems (section 9.6 Goldstein ed3). My specific problem is with understanding eq 9.104,         $\partial H = H(B) - K(A^{'}) $, where $\partial H$ represents the change in the hamiltonian under an infinitesimal canonical transformation (from the active view point ofc). The issue only arises for generating functions that explicitly depend on time.  Here's what I've thought of so far. I understand what $K$ is from the passive viewpoint (or so I think), its the hamiltonian that would furnish Hamilton's equations for the transformed variables $Q=q+ \delta q$ and $P = p + \delta p$. In the specific case of the generating function being a time dependent hamiltonian, $K = H + \delta t \frac{\partial H}{\partial t} = H + \delta t\dot H$, which makes sense because once you transform the variables to what they'll be in time $\delta t$, you'll also need to add on a term that comes from the Hamiltonian being at a later time $t+ \delta t$.   In the book, this is explained as a transformation depending on time changes the hamiltonian, so $H(A) \rightarrow K(A^{'}) $. Which I sorta get. But why not for $H(B)$? And what about the case when the Hamiltonian is time dependent and it is the generating function? Is $H(B)$ at a later time then?   Note: $A$ represents the original variables, $B$ is the transformed variables in the active sense, so in the same phase space as $A$, and $A^{'}$ is the same point as A but in the transformed phase space (passive). Do I have to recompile my application when I upgrade a third party jar? Can I use a USB stick for a normal install? (to get platform adaptability) So I know I can make a persistent LiveUSB whereby there would be anywhere up to 4GB (I think that's the max) of persistent storage for downloads, etc.  I am asking the opposite, in a sense. I'd like to configure a USB install to have the platform adaptability that a Live OS offers while fully utilizing the 120GB of space I have.  In essence I'm hoping to have a boot up install that reconfigures most/all the hardware/drivers as necessary every boot as I'd like to be able to boot off of it on nearly any machine. (Within reason - they will all be 64-bit)  The biggest gripe with doing multi-platform booting is the video driver stuff. Sometimes the system I'm booting off of is AMD, sometimes Nvidia, sometimes Intel.  Alternatively, a usable answer may be a way to better configure the LiveUSB setup for more storage utilization and customization. I got a UK visa for one month (restricted validity). It expires on November 4. Pakistani citizens are eligible to apply for a Turkish e visa if they have a valid UK visa. I want to visit Istanbul for a couple of days - from October 31 to November 2. Would I be eligible to still apply for an e visa?   My visa is for single entry. It's valid from October 4 to November 4. Why is uniq ignoring Unicode and lines with a single letter? I'm trying to combine both the American and British dictionaries into one large dictionaries, and I'm trying to remove all the duplicates from the superset, but it seems that uniq is not outputting words like, "épée" or single letters.  This is what I've tried using:  LC_COLLATE=en_US.UTF-8 cat american-english british-english |sort|uniq -u &gt; unique_sorted_combined_dict   If I just do this:  LC_COLLATE=en_US.UTF-8 cat american-english british-english |sort &gt; sorted_combined_dict   "épée" and other such words do show up, along with single letters.  Is there something I'm missing here with uniq?  I should note that I'm using uniq from the GNU coreutils on Ubuntu 12.10, if that makes any difference. What is the rule for adjective order? Why is current a scalar quantity? Does a charged particle accelerating in a gravitational field radiate? A charged particle undergoing an acceleration radiates photons.  Let's consider a charge in a freely falling frame of reference.  In such a frame, the local gravitational field is necessarily zero, and the particle does not accelerate or experience any force. Thus, this charge is free in such a frame. But, a free charge does not emit any photons. There seems to be a paradox. Does a freely falling charge in a gravitational field radiate? Password Reset for Users on a Multisite Subsite I am trying to prove that if I have $f:\mathbb{R} \to \mathbb{R}$ satisfying $\forall x,y\in\mathbb{R},f(x+y) = f(x) + f(y)$. Which is assumed continuous at $0$, that $f$ is continuous on $\mathbb{R}$  I am fairly sure it is, for that property seems to be a property of polynomials, and we know polynomials are continuous where defined(all reals)  Any ideas for rigor?  $|x-a| \lt \delta \implies |f(x+a)-f(x)-f(a)| \lt \epsilon$  No idea where to go from here, this is my first time doing $\epsilon-\delta$ stuff. If we minimize the Wasserstein loss, $$W_1 (P_S, P_T) = \underset{\gamma \in \Pi}{\text{min }} \sum_{x,y} |x-y|\gamma(x,y)$$ which means we are looking for the coupling $\gamma(x,y)$ that minimizes the cost of moving mass from the source distribution $P_S$ to the target distribution $P_T$,  Do the masses of the source and target distributions have to be identical? If so or not, how are the masses of $P_T$ and $P_S$ accounted for mathematically in, or when minimizing, the shown formula, or what might be missing/overlooked by the Wasserstein approach overall due to the mass differences? Recording iPad screen using QuickTime I need to record a demo on my iPad's screen where I narrate what's going on but I also want the sounds from the iPad to be in the video. It seems that choosing the Mac Built-in Mic option causes only my voice to be in the video while choosing the iPad Mic option cause only the sounds from the iPad to be in the video. What can I do to put both in the video?