Mean Definition and 1000 Threads

What do you mean by "countably infinite"? I just couldn't understand the meaning of countably infinite. I have seen some definitions but I couldn't get an insight. Could you please help me in understanding this term with some kind of an example? Thanks a lot. :)

I am supposed to use the mean-value theorem to show that lim_x→infty(√(x+5)-√(x))=0. Can anyone help me solving this problem? I have tried to set up the mean value theorem, but i just do not know how to proceed.

Hi, I have a question regarding quantum teleportation. I understand that Alice starts of with a photon A whose state she wants to teleport. Alice and Bob share an entangled pair of photons, B and C. Then Alice does something called a Bell measurement which entangles A and B and the result...

My QM book introduces operators like the momentum operator \hat{\mathbf{p}} which act on their eigenstates to produce new states like \hat{\mathbf{p}}|\mathbf{p}\rangle = \mathbf{p}|\mathbf{p}\rangle. But how can we interpret a state like that? How is multiplication between a Euclidean vector...

what do we mean by spin of a particle when we say it a point particle?how do we measure spin experimentally and give it values like +1,+2 etc. what does it mean by a spin 0 particle?

Wondering if it is possible to reconstruct a dataset if I give you the mean, median, standard deviation and N of a dataset. For example, if there are 20 students in a class. The mean of their exam score is 80, median is 85, standard deviation is 14. Of course the maximum score for the exam...

Suppose a person takes data (say counts per minute of cars going past his window), for a long time. Then he loses his data, but knows that he counted 5 cars more often than any other number. What is the likely range for the average count rate? I tried to solve this by saying the mode is 5, so...

Hello, Just had a question regarding statistical analysis. I'm trying to calculate the average of 4 numbers from a data set of 6 numbers in excel without manually choosing to average only the 4 numbers. e.g. 85 20 32 45 27 3 (total mean = 35.3 desired mean = 31) 100 30 27 40 21 1...

Let Pr(X_{i} = +1) =\frac{2}{3} = 1 - Pr(X_{i} = -1) , and S_{n} = \sum{X_{i}}, For each k≥1, define T_{k}\ =\ min \left\{n≥1: S_{n} = k \right\}. Calculate E[T_k], and Var[T_k]. 2. Homework Equations E[T_k] = \sum_{n=1}^{n=∞}{n Pr(T_k = n)} , and E[T_k]^2 = \sum_{n=1}^{n=∞}{n^2 Pr(T_k...

Hi, I am wondering how i can calculate the classical mean free path of electrons in InSb given the following material parameters... zero field conductivity = 1.86e4 1/ohm m electron mobility = 45,500 cm^2/Vs Is it a case of working out the scattering time and multiplying it by the...

Given f(n) = (1 - (1/n))n I calculate that the limit as n -> infinity is 1/e. Also given that x/(1-x) > -log(1-x) > x with 0<x<1 (I proved this in an earlier part of the question) I want to show that: 1 > (f(60)/f(infinity)) > e-1/59 > 58/59 I have tried using my value for f...

Other than the fan and hardrive, nothing else seems to be moving...

What exactly do we mean by nothingness?Im asking about when this universe was not present..not about space.

I learned the formulas F = G \frac{m_1 m_2}{r^2} and F = m \cdot a and also saw mathematically that objects have the same gravitational acceleration and will fall down at the same rate, also demonstrated in a video by people that were on our moon, even though one object clearly has more force...

If I you like Beethovens music does that mean that you "just dont just don't have the mental capacity to appreciate it yet" EDIT: ok the title was supposed to say "If I you DONT like Beethovens music does that mean that you "just don't have the mental capacity to appreciate it yet" ...

Homework Statement I am reading the Griffths book on quantum mechanics. In the first chapter on Momentum (Sect 1.5) what does d<x>/dt mean in the physical sense? Homework Equations NA The Attempt at a Solution If the expectation value <x> is already determined by the schrodinger...

Hi Guys, I am trying to measure variability in a part for my sensor which l do not know the true value. So l decided that a good way to measure variability in this case would be to measure precision of my data points as l change this part on the sensor. So l was wondering, can l compare the...

Hello, I have come across the following equation and want to know what the notation means exactly: \frac{-2 \pi \gamma}{\sigma} \frac{[ber_2(\gamma)ber'(\gamma) + bei_2(\gamma)bei'(\gamma)]}{[ber^2(\gamma) + bei_2(\gamma)]} Now, I know ber is related to bessel functions. For example, I...

I see this often and am not sure what it means. Suppose X and M are any two elements: X1-xMx Thanks.

Hi All, Is it possible to express the kurtosis \kappa, or the 4th central moment \mu_4, of a random variable X in terms of its mean \mu = E(X) and variance \sigma^2 = Var(X) only, without having to particularize to any distribution? I mean, an expression like \kappa = f(\mu, \sigma^2) or \mu_4...

I see this at a Wikipedia article: http://en.wikipedia.org/wiki/Cyanoacrylate

Homework Statement Let f(x)=log(x)+sin(x) on the positive real line. Use the mean value theorem to assure that for all M>0, there exists positive numbers a and b such that f(b)-f(a)/b-a=MHomework Equations f'(x)=1/x+cos(x) The Attempt at a Solution I know that as x→0, f'(x) gets arbitrarily...

Homework Statement Could anybody please explain this notation? The only thing I undersand here is the limit. Is r a superscript? If not, what is it? And what does E(variable|condition/equation) mean? I know that in the set theory, | means a separator between the variable and condition (ex...

Homework Statement This is no homework question, i could not understand a statement from the book Complex Numbers from A to ...Z because i don't know the meaning of the symbol used. Here is a screenshot: The problem is what does "n|q" mean? Any help is appreciated! :smile:

Hey there, not sure if I am posting this in the right place, so I apologize if I am not. So after some calculation I came up with an average human cell yielding 8.9876e+3 joules if annihilated. But what does that figure mean in the real world? I suppose I am looking for an analogy here...

I am going into third year (junior) in the coming fall and I plan to do some research over the summers with a prof I know. I've talked with the prof and he seems to be willing to take me on. However I have one concern is if I can graduate within four years. To make that happen, I have to...

What do you think the word "photon" used in textbooks and papers at present mean? - extended object which, when there are many of them, form light - point-like particle which, when there are many of them, form light - merely a short word for a _continuous_ change of energy of the field...

Homework Statement Mrs keely has 3 small children. She runs her washing machine every day, even on weekends.How much does it cost Mrs Keely to run a 2kWh machine per year? How many times is she running it 4, once or 2 (as the 3 small children count as 1 adult.)? The Attempt at a...

Hi, I have a random variable X with some zero-mean distribution. I have a function Y of this r.v. given by something complicated Y=(a+X)^\frac{2}{3} Is there an explicit way of finding the distribution of Y or even its mean? Thanks

I want to put the following as an axis label on a plot, but I cannot figure out how to get the bar on top in Matlab \bar \xi Thanks.

in this picture, there is a legend with the terms LINE and SINE in it http://i.imgur.com/IGJfm.png what do the terms LINE and SINE mean? I mean what do they stand for and what is their purpose in DNA. I have tried to look them up but it keeps going to math.

What does erf^(-1)(x) mean? erf^(-1)(.6) = ? Is there a value for erf, like there is for pi and e? is erf^(-1) same as 1/erf? I found out erf = error function...hmmm... THANKS for any explanations.

The wavefunction is defined on the domain of complex numbers. To find the probability of discovering a particle in a certain region, the amplitude of the wavefunction is integrated over that region. The problem is that you have an infinite set of complex numbers mapping to a single amplitude...

what does it mean to be momentum entangled? and how can it improve resolution? what does it mean to be momentum entangled? - say for photons and how can it improve the resolution of an optical microscope? Understanding polarization entanglement is easier/familiar - i.e. - the twins have...

I am reading the proof for the M.V.T, mostly understanding it all, except for this one step. Here is the link to it: http://tutorial.math.lamar.edu/Classes/CalcI/DerivativeAppsProofs.aspx#Extras_DerAppPf_MVT It's near the bottom of the page. What I don't precisely is why they create a new...

I need some help figuring out what these formulas mean and what they relate to. All I know is the 'upside-down triangle' symbol is known as a "Del", and it's used in vector calculus. Before the list of equations, it says "And God said...". After the list of equations, it says "...And there...

Dear all, I wonder if there is a function implemented in Mathematica to find the average value of a 2d function f(x,y). So averaged over a specified domain. Thanks in advance for any help! Sue

Homework Statement simply put, i got 2.1E+10 N.mm^5 for my steel beam experiment? but i am wonder, what conclusions can i make? 2. The attempt at a solution from online resouce, flexural rigidity is defined as the force couple required to bend a rigid structure to a unit curvature. so ...

Homework Statement What does this notation mean? I understand the $$\{x_t\}_{t = 0}^{\infty}$$ part, but I don't know what exactly $$U(x_0, x_1, ... x_n)$$ means. Does it mean that this function is a n+1 dimensional function, the same way f(x, y) is a 3 dimensional function? Homework Equations...

A million dollar to anyone who can tell me where that 1/r^(n+1) comes from in the second equality on page 3 of this pdf...

As the title already suggests, what does Newton's gravitational constant mean, and what it is, and how it is used in our universe? Hope you can help.

I've done a decent amount of reading on the subject, and I used this method of course when reporting errors during lab experience I got as an undergraduate, but it was never quite fully explained to me why exactly we report a value +/- the standard deviation of the mean as our result. Why not...

Components of angular momentum are also conserved in the case of a system evolving in an external conservative field with spherical symmetry where the resultant of all forces is radial i.e potential energy of the system depends only on radial coordinate.

OK, in the quantum eraser set up, you get a bump because of decoherence in the beam that does not pass through the double slit. In that beams causes the vector states of the left and right slit to be orthogonal. Even if you put the pi/4 POL in that beam, there would be two orthogonal states (the...

Homework Statement Frictionless, inviscous flow in a circular pipe. Velocity profile, v(r) = 6 - 6r^{1.828} Volume flowrate, Q = 9 \frac{\text{m}^3}{\text{s}} Pipe radius, R = 1 m Given velocities, v(0) = 6 m/s, v(R) = 0 m/s. Find mean velocity v_{av} 2. The attempt at a solution...

Homework Statement ##u(\omega) d\omega \propto \frac{(\hbar \omega) (\omega^2)}{e^{\hbar \omega \over k_B T}-1} d \omega ##Homework Equations The Attempt at a Solution ##\hbar \omega ## is the energy of a photon ##\frac{1}{e^{\hbar \omega \over k_B T}-1} ##and this is the density of states...

Hi, hopefully this is a simple question and easily answered. I've been doing some reading on the subject of mathematical modelling and examples of modelling reports. In one report, the failings of the model are put down to "dynamic forces". I've taken this to mean that there are external...

I bought physics for game programmers today to study ballistic impact, but I'm confused as to where a few numbers are coming from. I'm basically looking to understand what the values represent since the book does a bad job at telling me. I get that Ek = .5mv. In talking about the...

What does "couples as the 4th component of a vector" mean in the Dirac equation? I'm doing an exercise regarding the spin-orbit operator and the Dirac equation/particles, and I'm having trouble understanding the link between terminology and mathematics. The particular phrase I'm having trouble...

In several papers I read "L11 type Co-Pt ordered alloy" (see http://jap.aip.org/resource/1/japiau/v103/i7/p07E114_s1?isAuthorized=no , http://iopscience.iop.org/1742-6596/200/10/102002, http://www.sciencedirect.com/science/article/pii/0022024893903757). What exactly is meant by L11? Google...