I have a Toshiba laptop running Window XP (32) about 10 or 12 years old.  It is used at a model railroad club and its sole function is to run Java and an open source program called Decoder Pro.  It works great for our purposes but is getting dated as it no longer accepts updates.  I would like to use Ubuntu.  Which version should I use, etc.?
For a given hardware configuration, how do I find out if Ubuntu will run on it? What considerations should I take into account when choosing an Ubuntu version and  such as:    with a lighter desktop than the usual Gnome and Unity  with the even lighter LXDE desktop   Obviously Ubuntu does not run on some processor architectures. So how do I go about choosing the right version and derivate. How can I find out the minmal system requirements?
A clarification in a limit While reading this  I do not understand that how can we claim that there exist a polynomial with the properties, even if it exist then how is it same for the function and the inverse. Recently I saw a widget on the Stack Overflow website which says Stack&nbsp;Overflow now has its own currency called "unicoins". According to this widget, a user can earn reputation, customize Stack Overflow by changing its colors and the user can also remove the vote down button from their questions and answers by spending "unicoins".  This widget does not look real, because this is out of standard of the Stack Overflow website.  Also today is 1st April. Is Stack Overflow fooling us?  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Looking for a short story title about a "weird house" Where [if anywhere] should the apostrophe go in "three days work"? Which is correct?     1 Three day's work      2 Three days' work      3 Three days work   I would probably guess (2) is right, since the work belongs to the three days ("three days of work"). But I'm not sure. Would it be different if it was only one day? When I capture packets using the packet analyser wireshark while visiting  I can see packets that use the HTTP protocol (e.g.a GET request). My Get request uses 4 protocols: Ethernet II, IPv4, TCP and HTTP.  For the IPv4 I can see my own local IPv4 address of my pc as the source, for the destination I see the IPv4 address 91.198.174.225. When I go to this address in my browser I get to some wikipedia related website that says'wiki does not exist'. Why am I not seeing the Hydrogen article when I go to that ip address? Why is log-of-sum-of-exponentials $f(x)=\log\left(\sum_{i=1}^n e^ {x_i}\right)$ a convex function for $x \in\mathbb R^n$? How to prove $f(x)=\log\left(\displaystyle\sum_{i=1}^n e^{x_i}\right)$ is a convex function?  EDIT1: for above function $f(x)$, following inequalities hold:  $$\max\{x_1,x_2,\ldots,x_n\}\leqslant f(x)\leqslant\max\{x_1,x_2,\ldots,x_n\}+\log n$$  and I have tried proving its convexity via definition of a convex function with above inequalities, but that didn't work.  EDIT2: I have posted my answers below. Multicollinearity when individual regressions are significant, but VIFs are low I have 6 variables ($x_{1}...x_{6}$) that I am using to predict $y$. When performing my data analysis, I first tried a multiple linear regression. From this, only two variables were significant. However, when I ran a linear regression comparing each variable individually to $y$, all but one were significant ($p$ anywhere from less than 0.01 to less than 0.001). It was suggested that this was due to multicollinearity.  My initial research on this suggests checking for multicollinearity by using . I downloaded the appropriate package from R, and ended up with the resulting VIFs: 3.35, 3.59, 2.64, 2.24, and 5.56. According to various sources online, the point you should be worried about multicollinearity with your VIFs is either at 4 or 5.   I am now stumped about what this means for my data. Do I or do I not have a multicollinearity problem? If I do, then how should I proceed? (I cannot collect more data, and the variables are parts of a model that aren't obviously related) If I don't have this problem, then what should I be taking from my data, particularly the fact that these variables are highly significant individually, but not significant at all when combined.  Edit: Some questions have been asked regarding the dataset, and so I would like to expand...  In this particular case, we're looking to understand how specific social cues (gesture, gaze, etc) affect the likelihood of someone producing some other cue. We would like our model to include all significant attributes, so I am uncomfortable removing some that seem redundant.  There are not any hypotheses with this right now. Rather, the problem is unstudied, and we are looking to gain a better understanding of what attributes are important. As far as I can tell, these attributes should be relatively independent of one another (you can't just say gaze and gestures are the same, or one the subset of another). It would be nice to be able to report p values for everything, since we would like other researchers to understand what has been looked at.  Edit 2: Since it came up somewhere below, my $n$ is 24. Evaluating $\sum_{n=1}^{\infty}\frac{(n-1)!}{\prod_{r=1}^{n}(x+r)}$ for $x\in\mathbb{R}^{+}$ I am trying to evaluate the following sum. Here $x\in\mathbb{R^{+}}$. $$f(x)=\sum_{n=1}^{\infty}\frac{(n-1)!}{\prod_{r=1}^{n}(x+r)}$$ At present I do not know how to proceed. Any hints are appreciated. Thanks. I eliminated a computer player that had a strong religion (Buddhism). My religion was weak, whereas this other one was taking over the continent quickly. Now that I have him overrun, I want, well wanted, to work on converting cities to mine, but I see now that all of the cities period have his religion! I tried making an Inquisitor just to test, but he is ineffectual at removing Buddhism, being that I can only buy him in Buddhist cities. (Because all of my cities are Buddhist and my religion, Shinto, has been wiped out.   Is there no way to recover your religion in such a situation? Is there a way to recognize destructible environment in XCOM:Enemy Unknown? I'm studying machine learning and every book I open I bump into chi-squared distribution, gamma-function, t-distribution, Gaussian, etc.   Every book I have opened so far only defines what the distributions are: they don't explain or give the intuition on where the specific formulas for the functions come from.   For example, why is chi-squared distribution the way it is? What is the t-distribution? What is the intuition behind the distribution? Proofs? etc.   I would like to have a clear and fundamental understanding of the most commonly used distributions so that every time later on when I see them, I truly understand what is a t-distribution, what is a Gaussian distribution and most importantly why are they the way they are.   It would be nice if the books / tutorials  can explain the concepts to a layman so that in order to understand them you don't already need to understand them x) Many books are like this, they don't fit for beginners :( Is it possible to animate which characters of a text object are assigned to a material? Nvidia graphics card no longer works in Windows 10 (error: Code 43) but works in Ubuntu Let f be an r-cycle in $S_n$. Given any $h \in S_n$, show that $hfh^{-1} = (h(x_1), h(x_2), \dots, h(x_r))$ Let $f$ be differentiable at $x=a$.   Prove that if $x_n \to a^+$ and $y_n \to a^-$ then:  $$\lim_{n\to \infty} \frac{f(x_n)-f(y_n)}{x_n-y_n}=f'(a).$$  Every option that I think about seems to my very trivial, so I believe that I am doing something wrong.  Both numerator and denominator approach zero as $n\to\infty$ as the case of the formal definition of derivative, but it isn't guaranteed that the limits are equal (“$\frac{0}{0}$”).   Any direction? I have seen several answers and proofs here at MSE that a self-adjoint operator $T$ on a Hilbert space $H$ where $T^2=T$, implies $T$ being an orthogonal projection operator.   The thought struck me; what would happen if the condition $T^2=T$ is replaced by $T^3=T^2$ or instead by $T^4=T^3$ or why not more generally by $T^n=T^{n+1}$ for some $n\in\mathbb{N}$? Would this still imply $T$ to be an orthogonal projection operator?  I guess someone must have thought of this before me? In that case perhaps there is a reference in the literature for this or perhaps the proof is way simpler than I might expect? How to run adb and fastboot commands from Termux? For simple linear regression, the regression coefficient is calculable directly from the variance-covariance matrix $C$, by  $$ C_{d, e}\over C_{e,e} $$ where $d$ is the dependent variable's index, and $e$ is the explanatory variable's index.  If one only has the covariance matrix, is it possible to calculate the coefficients for a model with multiple explanatory variables?   ETA: For two explanatory variables, it appears that $$\beta_1 = \frac{Cov(y,x_1)var(x_2) - Cov(y,x_2)Cov(x_1,x_2)}{var(x_1)var(x_2) - Cov(x_1,x_2)^2} $$ and analogously for $\beta_2$. I'm not immediately seeing how to extend this to three or more variables. How to change from csh to bash as default shell I have csh as my default shell, as shown by echo $SHELL. I want to switch to bash as my default shell. I tried the following approaches to no avail:   With chsh I get:  chsh: can only change local entries; use ypchsh instead.  With ypchsh I get:  ypchsh: yppasswdd not running on NIS master host ("dcsun2").    I only have .chsrc in my home directory and I cannot find any .profile files in /etc. How can I change my default shell to bash? Does Microsoft Office 2010 have version control?  In other words, does it automatically save old versions of files?