Probability Given Datapoint Does Not Appear in a Bootstrap Sample?
Why on average does each bootstrap sample contain roughly two thirds of observations?
Why am I still being asked for an ssh password when I'm using private key authentication? There's already a question like this  so that my question could be considered duplicate, but I'll try to make my point clear that this is a different question.   Is there a way to derive  from the Lorentz' Force law or just from Maxwell's Equations?   The point is that we usually define, based on experiments, that the force felt by a moving charge on the presence of a magnetic field is $\mathbf {F} = q\mathbf{v}\times \mathbf{B}$, but in that case the magnetic field is usually left to be defined later.   Now can that force law be used in some way to obtain Biot-Savart law like we obtain the equation for the electric field directly from Coulomb's Force law?  I wanted to know that because as pointed out in the question I've mentioned, although Maxwell's Equations can be considered more fundamental, those equations are obtained after we know Coulomb's and Biot-Savart's laws, so if we start with Maxwell's Equations to obtain Biot-Savart's having use it to find Maxwell's Equations then I think we'll fall into a circular argument.   In that case, without recoursing to Maxwell's Equations the only way to obtain Biot-Savart's law is through observations or can it be derived somehow? In the 70's I had a stack of old Amateur Radio magazines (50s-60s), and for a long time I saved an article about using the  to combine a number of resistors to achieve a specific value. Does anyone recall and have a copy of this article, or know how the Euclidean algorithm is applied to solve this problem? Have you ever notice the sunset's image in the sea? It's like long light path to the end of the horizon! I've attached a sample of this:     How can we explain this? I know that it can happen even in wave less sea or lake! Why is this path so continuous? I expected that sea should act like a mirror! Volumes of n-balls: what is so special about n=5? The volume of an $n$-dimensional ball of radius $1$ is given by the classical formula $$V_n=\frac{\pi^{n/2}}{\Gamma(n/2+1)}.$$  For small values of $n$, we have $$V_1=2\qquad$$ $$V_2\approx 3.14$$ $$V_3\approx 4.18$$ $$V_4\approx 4.93$$ $$V_5\approx 5.26$$  $$V_6\approx 5.16$$ $$V_7\approx 4.72$$ It is not difficult to prove that $V_n$ assumes its maximal value when $n=5$.   Question. Is there any non-analytic (i.e. geometric, probabilistic, combinatorial...) demonstration of this fact? What is so special about $n=5$? I also have a similar question concerning the $n$-dimensional volume $S_n$ ("surface area") of a unit $n$-sphere. Why is the maximum of $S_n$ attained at $n=7$ from a geometric point of view?   note: the question has also been  for those curious to other answers. How to prove useful property of logarithm of generating functional in QFT? How to prove that $\ln(Z(J))$ generates only? I can't find the proof of this statement, and have only met its demonstrations for case of 2- and 4-point. How do I make an Bootable Ubuntu USB containing the the latest version of Ubuntu?  For completeness, how would I be able to do this on Ubuntu, Windows, OS X or another Linux distro? When you have a link from lets say twitter that is t.co/foo that links back to your website how does that effect SEO and how do the major search engines handle Shortened URLs? Why must a field whose a group of units is cyclic be finite? Do there exist general conditions under which we can conclude that continuity on a topological space is detected by $\mathbb{R}$? Whenever $X$ is a topological space, let us say that continuity on $X$ is detected by $\mathbb{R}$ iff for all functions $f : X \rightarrow Y$ where $Y$ is another topological space, we have that if every continuous function $c : \mathbb{R} \rightarrow X$ satisfies "$f \circ c$ is continuous", then $f$ is itself continuous.   Clearly, continuity on $\mathbb{R}$ is detected by $\mathbb{R}$ It is shown  that continuity on $\mathbb{R}^2$ is detected by $\mathbb{R}$. Clearly, it is not the case that continuity on $\mathbb{Q}$ is detected by $\mathbb{R}$, since every continuous mapping $\mathbb{R} \rightarrow \mathbb{Q}$ is constant.      Question. Do there exist general conditions underwhich we can conclude that continuity on a topological space is detected by $\mathbb{R}$? Do quest items weigh anything? Someone said that quest items don't count against your carrying capacity in Skyrim, even if they have a weight listed. Is this false? The recent  about a new supermassive virus being discovered got me thinking about how we define viruses as non-living organisms whilst they are bigger than bacteria, and much more complex than we first gave them credit for.   What biological differences between viruses and cellular organisms have made viruses be deemed non-living? Search All Fields In All Tables For A Specific Value (Oracle) What is going on in front of and behind a fan? Why is it that when you drop paper behind a fan, it drops, and is not blown/sucked into the fan, whereas if you drop paper in front of a fan, it is blown away? align xticks in PGFPlots Invoking JavaScript code in an iframe from the parent page Basically, I have an iframe embedded in a page and the iframe has some  routines I need to invoke from the parent page.  Now the opposite is quite simple as you only need to call parent.functionName(), but unfortunately, I need exactly the opposite of that.  Please note that my problem is not changing the source  of the iframe, but invoking a function defined in the iframe. Filter "Hot Network Questions" by excluding sites I was going to make a filter for the &quot;&quot; by excluding some sites from it.  I noticed  which talks about &quot;negative filtering&quot; but does not explain how one can do it or if it is possible.  There does not seem to be a way to do this, though.  On the filter page, my only options are:  So how can I do &quot;All sites except [list]&quot;? It would also be nice if this could include similar functionality with the meta checkbox.  Something like &quot;All main &amp; meta sites except...&quot; Let $x_0 \in \mathbb{R}$ and $f,g: \mathbb{R} \to \mathbb{R}$  such that $f$ is discontinuous at $x_0$ but $g$ is continuous at $x_0$, then $f+g$ at $x_0$ is...   My approach: After some graphical attempts to construct such a pathological case as given above I claim that the described scenario isn't possible. That is $$f \text{ disc. at } x_0 \text{ and } g \text{ cont. at } x_0 \implies f+g \text{ disc. at } x_0 $$  Proof: I was trying to come up with a contradiction, because if they happen to work out I find these kind of proofs to be most satisfying.   Assume $f+g$ is continuous at $x_0$ that is $$\forall \epsilon &gt; 0 ,\exists \delta_1 &gt; 0 : \forall x \in \mathbb{R}, |x-x_0| &lt; \delta_1 \implies |f(x)+g(x)-f(x_0)-g(x_0)| &lt; \epsilon  $$  Since this statement must be true for all $\epsilon &gt; 0$ I could choose $\epsilon:=1$. Next I know that also $g$ is continuous at said point $x_0$, thus  $$\forall \epsilon &gt; 0, \exists \delta_2 &gt; 0 : \forall x \in \mathbb{R}, |x-x_0| &lt; \delta_2 \implies |g(x)-g(x_0)| &lt; \epsilon $$  and I have that $f$ is NOT continuous at $x_0$ therefore: $$\exists \epsilon^* &gt; 0, \forall \delta&gt;0: \exists x \in  \mathbb{R}, |x-x_0| &lt; \delta \wedge |f(x)-f(x_0)| \geq \epsilon $$  My problem is to bring all these three statements nicely together. Mainly I get confused by the quantors. In order to match all three statements I assume I have to choose $\epsilon &gt; 0$ such that the last statement is met, so say $\epsilon:= \epsilon^*&gt;0$, so statement 1 and 2 are still true for said $\epsilon$  I also need to choose $\delta$. Lets say $\delta = \min{(\delta_1,\delta_2)}$ now I should be able to work with all three statements at the same time right? But then I stumble with my argumentation.  Let $|x-x_0|&lt; \delta$, then we obtain $$ |f(x)+g(x)-f(x_0)-g(x_0)| \leq |f(x)-f(x_0)| + |g(x)-g(x_0)| &lt; - \epsilon + \epsilon =0 $$ which means that $|f(x)+g(x)-f(x_0)-g(x_0)| &lt;0$ and I hope that this is a contradiction because $|.| \geq 0$. Please comment (or answer) if I am right or absolutely on the wrong path. I'd also appreciate it if you criticize my formulation. How do I complete "Find the Bitizen"? Getting attributes of Enum's value