Quickly Edit PDF Text

Quickly edit PDF text

It fully depends on a quality of your PDF document. If you've got a Pro version of Adobe Acrobat and the document was saved with proper settings (without minimizing a document's size) you can change the content directly in Acrobat Pro

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What is meant by PDF file?

PDF is a Portable Document Format. A PDF file is not easy to change once saved. Adobe Acrobat can do it

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How do I email this presentation to my teacher?

You should email it in PPT, which is Microsoft Power Point. PDF is Adobe Acrobat

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Reducing the file size of PDFs generated with CUPS-PDF

You can try changing the quality of the generated PDF. Edit the configuration file /etc/cups/cups-pdf.conf and change -dPDFSETTINGS=/prepress to -dPDFSETTINGS=/screenThe available options are:-dPDFSETTINGS=/screen (screen-view-only quality, 72 dpi images) -dPDFSETTINGS=/ebook (low quality, 150 dpi images) -dPDFSETTINGS=/printer (high quality, 300 dpi images) -dPDFSETTINGS=/prepress (high quality, color preserving, 300 dpi imgs) -dPDFSETTINGS=/default (almost identical to /screen)

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What does it mean for two random variables to have a jointly continuous PDF?

I think an analogy is the easiest way to demonstrate that $(X,Y)$ is not jointly-continuous. Consider a random variable $U$ which has a uniform distribution on $, delta]$. $U$ is a continuous random variable and has a pdf, $f_U(u) = 1/delta$ provided that $delta>0$. But as soon as you set $delta=0$, $U$ becomes a "degenerate" random variable which has a discrete distribution defined by $P(U=u) = 1$ if $u=0$ and $0$ otherwise.Now consider a bivariate extension of this. Let $X$ be any continuous r.v. and let $Y = X U$, where again $U$ is uniformly distributed on $, delta]$. It can easily be shown that the joint pdf of $(X,Y)$ is then $f_X,Y(x,y)=f_X(x) /delta$. If $X:=Y$, then that corresponds to the situation where $delta = 0$. But that would mean that the joint pdf is infinite at every point which violates the definition of pdf's. Thus, we are instead left with a "mixed-distribution" where one variable is continuous and the other is discrete

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Interpretation of joint pdf/product of marginal pdfs

I assume that this statement applies for specific values of $x,y$ because I am not sure that (b) or (c) is possible for all $x,y$. Also, the way you've written it here these must be discrete random variables (e.g. by use of the '=') so these are actually pmfs, not pdfs. That being said, first note that $P(X = x, Y = y) = P(X = x | Y = y) P(Y = y)$ (and similarly with the roles of $X$ and $Y$ reversed). So: (a) implies that $P(X = x | Y = y) = P(X = x)$, which is the definition of independence. That is, knowing that $Y = y$ tells us nothing about the event $X = x$. (b) implies that $P(X = x | Y = y)

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Embedded PDF images in PDF output not selectable / can't be copied

Technically, this is PDF-viewer-specific. In practice, however, it seems to be OS-specific: On MacOS, all PDF viewers (Preview, Skim, .) but Acrobat put snapshots as vector images into the clipboard (and from there it is easy to export them into stand-alone PDF files). The reason is probably that PDF is the native clipboard format for vector graphics on MacOS (opposed to WMF/EMF on Windows), so the GUI toolkit of the OS supports this out of the box. Generally, something like this should be possible for Adobe as well. However, I always have had the impression that Adobe intentionally does not support a feature like that - given that even their bitmap snapshots feature only a ridiculously bad resolution. (My workaround for this problem - back in my Windows days - was to use a 24" screen, zoom the figure of interest in Adobe Reader so that it takes the full screen, and then copy the whole screen. Still a bitmap, but at least the resolution was a lot better.)In fact, the flexible PDF handling was a major reason to switch to MacOS (even though there are a lot of things I really do not like about this system).