Who and That : Pronouns or Relative Pronouns
How to use "who" vs. "that"
Can anyone explain to me why I would want to use IList over List in C#?  Related question: The classic example... $X \sim Po\left (\lambda\right ), Y \sim Po\left (\mu\right)$, X and Y are independent.  Show that the conditional distribution of X is binomially distributed. Or in other words, $P(X=k\mid X+Y = n) = P (\tilde{X} = k), \tilde{X} \sim B\left (n ,\frac{\lambda}{\lambda + \mu}\right )$.   I've so far managed to reach to this step, and have been stuck since. Just somehow gotta get a $\frac{1}{n!}$ in the denominator, that would then complete the proof..or at least I think..  $$P(X=k\mid X+Y=n) = \frac{\frac{\lambda^{k}\mu^{n-k}}{k!(n-k)!}}{P(X+Y = n)}=  \frac{\frac{\lambda^{k}\mu^{n-k}}{k!(n-k)!}}{\sum_{i=1}^{n} \frac{\lambda^{i}\mu^{n-i}}{i!(n-i)!}}$$  Thanks for the help! What is the proper way to explain the twin paradox? The paradox in the  is that the situation appears symmetrical so each twin should think the other has aged less, which is of course impossible.  There are a thousand explanations out there for why this doesn't happen, but they all end up saying something vague like it's because one twin is accelerating or you need general relativity to understand it.  Please will someone give a simple and definitive explanation for why both twins agree on which twin is younger when they meet for the second time? If the sum of $n$ cubes is zero, then the sum must be no larger than $\frac n3$. Assume that $a_1,...a_n$ are real numbers and $-1 \leq a_i\leq 1$ for $1\leq i\leq  n$. If $$a_1^3+\ldots +a_n^3=0$$ Then show that $$a_1+a_2+\ldots+a_n\le n/3$$   I just came cross this problem the other day. I totally have no idea how to prove it. Are there any hints about which theorem, principle or method to apply? Maximum Likelihood Estimation (MLE) in layman terms Could anyone explain to me in detail about maximum likelihood estimation (MLE) in layman's terms? I would like to know the underlying concept before going into mathematical derivation or equation. How to install all possible media codecs from console?  Is there a way to load and save them for some cases without Internet connection?  Thanks in Advance! Isomorphism of factor groups I came across an intuitive statement on factor groups that I realized I did not know how to prove.   Let $G$ be a group, and let $H \unlhd G, K \unlhd G$ such that $H \cong K$. I want to show that $G/H \cong G/K$.   I'm not sure how exactly to construct such an isomorphism from an isomorphism $\varphi: H \to K$. Is that the correct approach? By extending such an isomorphism to an automorphism on $\varphi^{\uparrow}:G \to G$, then we could apply the First Isomorphism Theorem to the composition of the natural homomorphism $\mu: G \to G/K$ and that automorphism (for $\ker \mu\varphi^{\uparrow} = H$, if such a $\varphi^\uparrow$ exists).  Edit: Hamou points out this is false in the infinite case: can it still be salvaged in the finite case? Are there restrictions we can put on $G, H,$ and $K$ such that this is true? individual tick label style with pgfplots given the following code, I want to modify the tick labels in such a way, that for negative values of x, the labels are located above the x-axis. How can I realize this?  \documentclass{report} \usepackage{pgf} \usepackage{pgfplots} \pgfplotsset{compat=newest} \pgfplotsset{plot coordinates/math parser=false} \begin{document} \begin{tikzpicture} \begin{axis}[% axis x line=middle, axis y line=middle, width=10cm, height=10cm, scale only axis, xmin=-5, xmax=5, xtick={-4, -2, 0,  2,  4}, xticklabels={$-4\pi$, $-2\pi$, $0$, $2\pi$, $4\pi$}, extra x ticks={-4, -2}, ymin=-1.4, ymax=1.4, ytick={-1,  0,  1}] \end{axis} \end{tikzpicture}% \end{document} Linear regression in a loglog-plot with fixed slope Goal: create a plot to compare the empirical convergence rate of a numerical method with the one expected from the theory.  Accordingly, given a loglog-plot, I would like to add the line which has a prescribed slope (in this case, the convergence of the method) and the best intercept to fit the data (e.g., in a least-square sense).  Question: how to do a linear regression with fixed slope in pgfplots?  What I have done so far is the following: (1) compute the regression line (of the logarithm of the quantities), (2) save the intercept, (3) plot the line with the slope expected from the theory and this intercept.  This is a good approximation of what I am looking for, provided the data are in agreement with the theory.  Thanks  MdFB Hyperlinks to web sites using anchors sometimes don't work Trigonometry question finding the sin and tan If angle $\alpha$ is reflex, and $\cos \alpha = -\frac{9}{41}$, without using a calculator, evaluate  (a) $\sin \alpha$ (b) $\tan \alpha$ (c) $\cos (\alpha - 180\deg)$     . Does assumption of normality of each mixture components implies that each margins is normal I just would like to understand some information about the joint normality and the margins. I read that the normal joint distribution almost always implies that the univariate margins are all normal.   My question is:  1- Is this apply for Gaussian mixture models? For example, in the Gaussian mixture model, each mixture component follows a Gaussian distribution. Hence, does it imply that each margin will be a Gaussian distribution as well? "I understand that mixture components are used to describe the dependency structures, and they are the joint distribution. is that correct?  2- I read this from one answer to a question in this site . "So yes, the assumption of joint normality is a sufficient condition for all marginal distributions to be normal, irrespective of the dependence structure. Hence, the theory of Copulas does not affect this result in any way."  However, I really do not understand this: irrespective of the dependence structure. As I understand if the joint distribution in normal then the dependence structure is normal.   Could someone help me with my questions, please? Atmospheric lighting in cycles How would I go a about making volume light beams?  I have have tried  various tutorials, but they must be for a older version. as applying them does seemingly nothing.  A link to a functioning tutorial would be greatly appreciated as well.  I don't have a picture or .blend to show, as my problem with atmospheric lighting does not pertain to any specific scene. Can I do anything about a Nikon d750 taking 5 minutes to power on after taking saltwater damage? I have had a Nikon d750 for a year or so, and 6 months ago it took on a bit of saltwater damage. It still works, but twice in the past it wouldn't power on, once for two weeks and once for two days.   Now it is at a point where it takes around 5 minutes to power on, and when i switch the camera to 'off' or standby, it completely powers off as if the battery drops out, then it takes another 5 mins or so for it to power back on, if it does at all. So I have switched the standby timer in the settings to 'infinity' so it just stays powered on.  I am taking it in to have it looked at, I just hope the damage isn't too fatal. I wonder if anyone has experienced anything similar to this, or can help me diagnose the actual problem. I have tried different batteries, and everything else possible really. Camera itself works fine, just power issues.  thanks in advance. How can I convert my Java program to an .exe file? I am trying to understand   How can a set contain itself? Can you show example of set which is not a set of all sets and it contains itself. Is it possible to make LaTeX mark overfull boxes in the output? Is it possible to make LaTeX mark overfull boxes in the output, for example by drawing red rectangles in the PDF where the boxes overflow? The purpose -- to more easily "see" where the problems are in the output. This is a  about how to handle email sent from your server being misclassified as spam.  For additional information you may find these similar questions helpful:                    Sometimes I want to send newsletters to my customers. The problem is, that some of the emails get caught as spam messages. Mostly by Outlook at the client (even in my own Outlook 2007).  Now I want to know what should be done to create "good" emails. I know about reverse lookup etc., but (for example), what about a unsubscribe link with an unique ID?  Does that increase a spam rating? How do I boot into recovery mode? Can a ultracentrifuge be used to test general relativity? With today's ultracentrifuge technology, they can spin so fast that the sample can be subjected to  accelerations of up to 2 millions Gs. That is equivalent to two solar masses. Has someone tried to measure the time dilation in a radioactive sample? How calculate that time dilation respect to the time outside the ultracentrifuge, for example one week. I think that that time dilation will be significant enough to be measured.