Integral of the inverse of a CDF is the mean of the PDF?
Expected value as a function of quantiles?
Is there any way to increase the drop rate of items? Why is there an extra plastic container in my toilet tank? I have an ArrayList&lt;String&gt; that I'd like to return a copy of.  ArrayList has a clone method which has the following signature:  public Object clone()   After I call this method, how do I cast the returned Object back to ArrayList&lt;String&gt;? C++ 11 Thread initialization with member functions compiling error How to put a full stop at the bottom, not mid-line, after an aligned matrix? Show that $x^{n-1}+\cdots +x+1$ is irreducible over $\mathbb Z$ if and only if $n$ is a prime. How do I derive the Lorentz contraction from the invariant interval? Reviewing some basic special relativity, and I stumbled upon this problem:  From the definition of the proper time: $$c^2d\tau^2=c^2dt^2-dx^2$$ I was able to derive the time dilation formula by using $x=vt$: $$c^2d\tau^2=c^2dt^2-v^2dt^2=c^2dt^2\left(1-\frac{v^2}{c^2}\right)\rightarrow d\tau = dt\sqrt{1-\frac{v^2}{c^2}}=t/\gamma$$  Now, I would very much like to be able to derive the length contraction formula in a similar fashion, and feel strongly that this should be possible. The definition of the invariant interval is: $$ds^2=dx^2-c^2dt^2$$ using $t=\frac{x}{v}$ I tried: $$ds^2=dx^2-\frac{c^2}{v^2}dx^2=dx^2\left(1-\frac{c^2}{v^2}\right)\rightarrow ds=dx\sqrt{1-\frac{c^2}{v^2}}$$  This is where I'm stuck: I don't see how this can be converted to a Lorentz factor...  Any help that will allow me to arrive at the desired result $ds=\gamma dx$ would be very much appreciated. Alternate exits in Bit Trip Runner 2 Is there any point in taking the alternate exits in Bit Trip Runner 2?  I can't see any benefit to doing so in terms of unlocking a different path in the overworld, so is it just for your own benefit? I often run into this issue. I'm creating a file in Photoshop with masked layers etc. I want to make the final output available for some mock-ups in Illustrator, so I rasterize the layers and marquee select the entire area, copy and move to Illustrator.  Pasting the area in Illustrator flattens all transparencies, which is quite annoying. I'm left with my object and a flat white background.  Is there a reason for this? When I include a  \usepackage{forest} all colored text title, section headings disappears with IEEE Access journal template How can I tackle this problem? I think we all understand the necessity of delete when reassigning a dynamically-allocated pointer in order to prevent memory leaks. However, I'm curious, to what extent does the C++ mandate the usage of delete? For example, take the following program  int main() {      int* arr = new int[5];      return 0; }   While for all intents and purposes no leak occurs here (since your program is ending and the OS will clean up all memory once it returns), but does the standard still require -- or recommend -- the usage of delete[] in this case? If not, would there be any other reason why you would delete[] here? Suppose $\int_{[a,b]}f=0,\text{ then }f(x)=0 \forall x\in[a,b]$ Let $a&lt;b$ be real numbers. Let $f:[a,b]\to\mathbb{R}$ be a continuous non-negative function. Suppose $\int_{[a,b]}f=0,\text{ then }f(x)=0 \forall x\in[a,b]$    Proof: Suppose for the sake of contradiction $\exists x_0\in[a,b] \text{ such that } f(x_0)= D&gt; 0$  Since the function is continuous at $x_0$, we have $$\forall \epsilon&gt;0, \exists \delta&gt;0 \text{ such that } |f(x)-f(x_0)|\leq\epsilon\text{ whenever } x\in[a,b]\cap(x_0-\delta,x_0+\delta)$$ choose $\delta=\delta_1$ such that $\epsilon=D/2$, then we can say: $$-D/2 \leq f(x)-f(x_0)\leq D/2$$ $$-D/2 \leq f(x) - D$$ $$f(x)\geq D/2&gt;0$$ This implies that $\int_{[a,b]\cap(x_0-\delta_1,x_0+\delta_1)}f &gt;0$  Now since $\int_{[a,b]} f = 0$. we have  $$\int_{[a,b]}f=\int_{[a,x_0-\delta_1]}f+ \int_{(x_0-\delta_1, x_0+\delta_1)} f + \int_{[x_0+\delta_1,b]}f=0$$ $$\int_{[a,x_0-\delta_1]}f+\int_{[x_0+\delta_1,b]}f&lt;-D/2,$$ but this is a contradiction since $f(x)\geq 0$ and hence $\int_{[a,x_0-\delta_1]}f+\int_{[x_0+\delta_1,b]}f\geq 0$  Is my proof correct? Can't get my model out of wireframe mode I'm new to Blender and this site, so I apologize in advance if I'm not following any of the proper etiquette.  I'm no artist, but I'm trying to learn Blender so that I have some programmer art for me to work around in Unity.    I followed a tutorial for making a basic human model, I rigged it with rigify, and now I'm starting to export it following yet another tutorial.  The thing is, when I was trying to rig the model, I couldn't get the model to go transparent so that I could see the bones inside the model.  Eventually, I managed to get it into wireframe mode, but I can't get it back into solid mode.    It's probably just a display thing and not a property of the model itself, but I want to be sure.  I'm looking at the display options under the "Figure" pane in Blender, and none of the Display check boxes are checked, including the one that says "Wire".  I don't want to import a plain wireframe model into Unity, and even if that doesn't happen, this is functionality of Blender that I should really know anyway, so I'd appreciate any help that anyone has to offer.  If necessary, I can upload the .blend file, but I'm not sure what site people would prefer that I upload it to. Is there a word for capitalizing in the middle of a word, as in "eBay"? Usually this sort of word is a trademarked name, such as eBay or BlackBerry.  Is there a word that describes capitalization mid-word? How to use `ybar interval` without skipping the last value I have the following code  \documentclass[tikz]{standalone} \usepackage{pgfplots} \usepackage{pgfplotstable} \usepackage{filecontents}  \begin{filecontents}{testdata.dat}   -3.316988309367815e-07 0.07000000000000001   -1.948815911147526e-08 0.13   7.15864175355987e-08 0   1.799432483450127e-07 0   0.0002850606647384129 0   0.0009429559686380238 0.08999999999999997   0.00157188462064142 0   0.005259918700865051 0   0.01739392641273605 0.18   0.06208364670743995 0.55   68.69485148165926 6.970000000000001   31.217611224923 79.12   0 12.89 \end{filecontents}  \pgfplotsset{compat=newest} \pgfplotstableread{testdata.dat}\datatable  \begin{document} \begin{tikzpicture} \begin{axis}[   ybar interval,   width=10cm,   height=5cm,   enlargelimits=false,    xtick=data,   ymin=0, ymax=100,   xticklabels={0 -- 0.063,0.063 -- 0.125,0.125 -- 0.25,0.25 -- 0.5,0.5 -- 1,                1 -- 2,2 -- 4,4 -- 5.6,5.6 -- 8,                8 -- 11.2,11.2 -- 16,16 -- 22.4,22.4 -- 31.5},   x tick label style={rotate=60,anchor=east}   ]   \addplot table[x expr=\coordindex,y=0]{\datatable};   \addplot table[x expr=\coordindex,y=1]{\datatable};  \end{axis} \end{tikzpicture} \end{document}   and the output looks like this:    But the command ybar interval does skip the last value. It should look like:    I prefer to have the last value to show up in the interval 22.4 -- 31.5. How do I achieve this without inserting a row of zeros to my table? How do I convert a video to GIF using ffmpeg, with reasonable quality? I'm converting a video to GIF file with ffmpeg:  ffmpeg -i input.flv -ss 00:00:00.000 -pix_fmt rgb24 -r 10 -s 320x240 -t 00:00:10.000 output.gif   It works great, but output gif file has a very low quality.  Any ideas how can I improve quality of converted gif? Should your PhD students call you by your first name? Add bst file with LaTeX / MiKTeX I'm trying to use elsarticle-num-ident.bst, an exact copy of  C:\Program Files (x86)\MiKTeX 2.9\bibtex\bst\elsarticle\elsarticle-num.bst    but every time I run LyX, I get the bibtex error  I couldn't open style file elsarticle-num-ident.bst   This is despite reconfiguring LyX and restarting, and despite running MixTex's Settings/Options' "Refresh FNDB" as Administrator.  It also doesn't work if I put the .bst file in the same folder as the .lyx file.  How should I help lyx/bibtex/Mixtex find the .bst file?  Once I get the identical copy to work, I plan to edit it to not print URLs, as suggested .  Related questions: Can the editor for editing tag descriptions get updated to match the normal questions/answers editor? The text editor that is shown when editing tag descriptions still uses the previous behaviour for inserting links and images. Also, the placeholder text for links is still http:// instead of https:// compared to the new editor. Another &quot;nice to have&quot; feature that exists in the main editor is the ability to paste an image from clipboard directly to the text editor without having to press the &quot;insert image&quot; toolbar-icon first. Can it get updated to match the editor we use for questions and answers?  The following screenshot is an example of how it looks if I try to insert a link for a tag description:  In comparison, this is how it looks in the new editor: Simple: every other race in Middle Earth has rings, why do Hobbits and Orcs not?