Note: I edited this question on 1/1/2018  because of the comments on the original question.  So some comments relate to the earlier version. It is closed as duplicaten but I dusagree with that   For a bi-variate normal distribution with mean $(\mu_X, \mu_Y)$, variances $\sigma_X^2, \sigma_Y^2$ and correlation $\rho$ it holds (see e.g. , ) that   $$\Bbb E(Y\mid{X=x})=\mu_Y + \rho \frac{\sigma_Y}{\sigma_X}(x-\mu_X)$$  By symmetry I would say that (is this correct?)   $$\Bbb E(X\mid{Y=y})=\mu_X + \rho \frac{\sigma_X}{\sigma_Y}(y-\mu_Y)$$  Next question:  These are two lines in an $(x,y)$ plane.   The picture below shows and example of a sample from such a bivariate normal distribution.  Conditioning on $X$ means that I 'intersect' along the red lines, conditioning on $Y$ is 'intersecting' along the blue lines.     The contours of constant density for a bi-variate normal distribution are (rotated) ellipses.      Note that the rotation angle of the prinicipal axis wrt to the   $x$-axis depends on the correlation $\rho$ (so, as opposed to what   @whuber says in his comments below) correlation is the relevant   topic here. Because, as argued by @MichaelHardy, there are values for   $\rho$ where these lines correspond to these principal axis.      My question is whether the two lines of the conditional means   correspond to (one of) the principal axes of these ellipses and if not   how this can be explained geometrically.   Note: this question is not answered by the answer of @DilipSarwate here (and which I fully agree with) :  because he is using OLS (so regression techniques).  The above formula are a theoretical property of the bivariate (multivariate) normal distribitions namely that all conditional distributions of it are also normal (see ), there is no need for referring to regression of OLS to show that.
Let's say that there exists some "true" relationship between $y$ and $x$ such that $y = ax + b + \epsilon$, where $a$ and $b$ are constants and $\epsilon$ is i.i.d normal noise. When I randomly generate data from that R code: x &lt;- 1:100; y &lt;- ax + b + rnorm(length(x)) and then fit a model like y ~ x, I obviously get reasonably good estimates for $a$ and $b$.  If I switch the role of the variables as in (x ~ y), however, and then rewrite the result for $y$ to be a function of $x$, the resulting slope is always steeper (either more negative or more positive) than that estimated by the y ~ x regression. I'm trying to understand exactly why that is and would appreciate it if anyone could give me an intuition as to what's going on there.
Is it possible to nest a 'find -exec' within another 'find -exec'? Something like the following is what I what I'm after,  but my code doesn't work, no matter how I escape {} and + ;     find ./ -maxdepth 1 -type d -name '.*' -exec \     find {} -maxdepth 1 -type f -name '*.ini' -exec \         md5sum \{\} \\; \;   After seeing this ,  I found that the following code works, but it isn't nesting find as such, and I suspect there is a better way to do this particular job.       find ./ -maxdepth 1 -type d -name '.*' \ -exec bash -c 'for x; do     find "$x" -maxdepth 1 -type f -name "*.ini" \     -exec md5sum \{\} \;; \ done' _ {} \+   Is there some way to nest find -exec without the need to invoke  a shell (as above), with all its whacky quoteing and escape constraints?    Or can this be done directly in a single find command,  using a blend of its many parameters? What is difference between int.class and Integer.TYPE in java? Does the harmonic series converge if you throw out the terms containing a $9$? I found this very amusing comic on the internet the other day:   The last frame seems to claim that the harmonic series converges if you throw out all the terms with a $9$ in the denominator. Is this true? Where could I find a proof? Is it only true for terms with a $9$ or is it true for any number? If it's only true for $9$, why is that? If $\gcd(a,b)=1$, then there exists integers $x$ and $y$ such that $xa + yb = 1$ Did not find this from this website...  If $$ \gcd(a,b)=1,$$ then there exists integers $x$ and $y$ such that $$xa+yb=1.$$  Now, the tip is to use particular corollary, that states:  The class $[m]_{n}$ generates $\mathbb{Z}/n\mathbb{Z}\Leftrightarrow \gcd(m,n)=1.$  I am totally lost with the corollary.  Let's assume that $\gcd(m,n)=1$. Then, $[m]_{n}$ generates $\mathbb{Z}/n\mathbb{Z}$.  OK! Then what?  There is also follow up, where I have to prove the converse. I am familiar with Bezout's lemma. Mean and variance of inverse of a normal RV My random variable $X$ is normally distributed with mean $b$ and variance $p$. I defined a new RV, $Y$, such that $Y=1/X$. Does anyone know how to find the mean of $Y$ and $Y^2$? Tool to manage and/or make available a list of my publications on the web? Live USB for installation does not boot, black error screen followed by visual artifacts on a purple screen Create instance of generic type in Java? Getting an error in W3C Markup Validation when trying to get a whole  element as a link in a page finding rational roots of polynomials How many files can a windows folder contain?  This question is asked  but then the question text pollutes the question with issues of "rules of thumb"  So to be clear, this question is: How many files can a windows folder contain? How to switch from Natbib to Biblatex in pre-made document class/template? I am using  to write my thesis. The template uses Natlib for references, whereas I really need Biblatex.   When I simply try to change \usepackage[natbib] for biblatex I get the error message  This is BibTeX, Version 0.99d (TeX Live 2016/Debian) Capacity: max_strings=100000, hash_size=100000, hash_prime=85009 The top-level auxiliary file: aagot-1-report.aux The style file: acm.bst Illegal, another \bibstyle command---line 80 of file aagot-1-report.aux  : \bibstyle  :          {acm}  I'm skipping whatever remains of this command Database file #1: Mendeleytry.bib.bib Warning--I didn't find a database entry for "" You've used 14 entries,code here   The solution  \usepackage[backend=bibtex, natbib=true, style=numeric]{biblatex}   didn't work.  Another possible solution was said to be to recompile from scratch to delete the .aux file, but that resulted in  /usr/share/texlive/texmf-dist/tex/latex/biblatex/biblatex.sty:462: LaTeX Error:  Command \bibhang already defined.            Or name \end... illegal, see p.192 of the manual.  See the LaTeX manual or LaTeX Companion for explanation. Type  H &lt;return&gt;  for immediate help.  ...                                                l.462 \newlength{\bibhang}   I have tried to use this "marco" to override the \requirePackage settings, but that also didn't work and resulted into  LaTeX Error: Two \documentclass or \documentstyle comm ands.  See the LaTeX manual or LaTeX Companion for explanation. Type  H &lt;return&gt;  for immediate help.  ...                                                l.45 \documentclass[whitelogo]{                            tudelft-report}    Where I can't seem to delete any of the document classes without getting the functionality of the tudelft-package and the biblatex citing (or in fact getting it to work at all!)  (no line number): [0] Config.pm:343&gt; INFO - This is Biber 2.5 [0] Config.pm:346&gt; INFO - Logfile is 'aagot-1-report.blg' [62] biber:290&gt; INFO - === Tue Apr 24, 2018, 22:24:06 [246] Utils.pm:165&gt; ERROR - aagot-1-report.bcf is malformed, last biblatex  run probably failed. Deleted aagot-1-report.bbl [246] Biber.pm:113&gt; INFO - ERRORS: 1   Is there any way I can still make this template work with Biblatex? Natlib seems to deeply rooted in the file and I don't know how to change it/access the settings/the ".sty"-file. Can I use the example documentclass combined with biblatex (instead of the standard natbib) without losing the great parts of the rest of the document class?  Thanks very much :) How can I convert a hex string to a byte array? Deserializing JSON when sometimes array and sometimes object I want to shrink my second (LVM) partition, in order to create a new partition in the newly freed space. I am using the Live CD to do so, because I know I can't resize/move this partition while it is in use. When I opened GParted in the Live CD, I realized that I could not resize the partition, because when I right-click it, the option "resize/move" is disabled.  I tried to unmount it, to "lazy" unmount it (umount -l /dev/sda2) but it didn't work.  A screenshot from GParted: Prove that : $$\sum_{k=0}^{\infty} \frac{(-1)^{k}}{(2k+1)^3}=\frac{\pi^3}{32}.$$    I think this is known (see ), I appreciate any hint or link for the solution (or the full solution). Hyphen or no hyphen when modifying an adjective with a quantity? My thinking:    acceleration corresponds to a force which is instantaneous, so the acceleration of a rigid body can be rather spiky (non-smooth) velocity (angular velocity) describes the ratio of change of the distance(angle), so it is smooth in the real world.   Conclusion, it makes sense to  (e.g., simple averaging) a velocity signal (temporal velocity), but it does not make so much sense to do smoothing on acceleration signal. Am I right? How to create animated GIFs of prototype mockups, like the ones on Dribbble? I'm sure you've seen Dribbblers upload animated mockups of their designs.   Here's an example:     I can create mockups on Photoshop and even apply simple Tween Animations to them but I can never get my GIFs to look like the example here.   What are Dribbblers using to create these animations?   Notice that the animations also include touch points and perfect motion. I would like to convert my Photoshop mockups to do the same.  How can I create an animated example of my mockups, similar to the ones created by Dribbblers? What is the word that is used to describe the oversimplification or non-academic discussion of a complex issue?   Typically, I'm looking for a word like pedantic, or puerile, except that the word covers the fact that the discussion is particularly non-academic. I know that such a word exists since I have used it before, but it has skipped my mind.