Distribution Definition and 1000 Threads

In statistical mechanics the boson distribution function has the well known form ##f = \frac{1}{e^{E/T} - 1},## (in the special case of zero chemical potential). As one considers the non-equilibrium variant this generalize to ##f = \frac{1}{e^{\frac{E}{T(1+ \Theta)}} - 1},## for some function...

Homework Statement Using Darcy’s law, plus another appropriate relationship, derive a single equation for the pressure distribution in a porous material. Your equation should be stated in terms of generic operators (i.e. without assuming any specific coordinate system) and allow for the fact...

I have an asymetric probability distribution function (pdf), in this case we know that the concept of an error bar does not seem appropriate. Well I'm finding the shortest interval that enclosed the 68% of probability. My problem is that my pdf couldn't be integrated analytically and I'm using...

Homework Statement A spherical charge distribution is given by p = p_0 (1- \frac{r^2}{a^2}), r\leq a and p = 0, r \gt a , where a is the radius of the sphere. Find the electric field intensity inside the charge distribution. Well I thought I found the answer until I looked at the back of...

A mode of frequency ##\nu## has energy ##E_n = h \nu##. In terms of photons, the interpretation that I have read several places, is that this correspond to ##n## photons of energy ##h \nu##. Furthermore, it is stated that the probabilty of finding ##n## photons at frequency ##\nu## is given by...

Homework Statement Hi all - I have been trying to evaluate part II of this problem for a long time now... For a simplified model of a proton's charge distribution, Find the constant of proportionality required to normalise ρ correctly. Show that Homework Equations N/A The Attempt at a...

Homework Statement Two test charges are located in the x–y plane. If q1 = -3.50 nC and is located at x = 0.00 m, y = 0.680 m and the second test charge has magnitude of q2 = 3.60 nC and is located at x = 1.00 m, y = 0.650 m, calculate the x and y components, Ex and Ey, of the electric field, ...

Background: I am trying to write a program for Buckingham Pi Groups. I need to find a way to list all the input varialbes as different sets. For example if I have 4 variables [V D p u] and I want to distribute them 3 ways I get 4 sets. Number of Sets = Binomial(Number of Variables...

Homework Statement You throw a coin a 100 times, what's the probability of getting 50 tails? Homework Equations The Attempt at a Solution We have n=100 , p=1/2, q=1/2 and k=50 we substitute in the first equation we get: P= 100!/ (50! * 50!) * (1/2)^100 The factorials are not simple to...

I'm going over the Physics GRE and this question has me a little confused. The configuration of the potassium atom in its ground state is 1s2 2s2 2p6 3s2 3p6 4s1. The answer to which of the following is true is this statement: "Its electron charge distribution is spherically symmetrical." Is...

So, the exercise is to find the expected value of following distribution: f(x) = 0,02x 0<x<10 answer in the book says 6,67 As far as I knowe, the expected value is calculated by the Integral of x * f(x) between 0 and 10, in this case! It looks like this won't give the result 6,67! what am...

If \(Y = -X\) and \(X\sim Ber(1/4)\), then what is Y? I know that \[ X\sim \begin{cases} 1 - p, & x = 0\\ p, & x = 1 \end{cases} \] where \(p = 0.25\) in this case. What is the negative of \(X\) though. It doesn't make any sense making the probabilities negative.

Homework Statement i need to show that the peak of the maxwell Boltzmann distribution is equal to 1/2 kt. Homework Equations maxwell Boltzmann distribution according to modern physics 3rd edition by kenneth kramer. ill try to do my best with this N(E)= \frac{2N}{√∏}...

In carrom game, we have black/white small disc pieces, just imagine we have a single piece of it on the board.We hit that pieces with a striker on one side of the four wall. And the pieces goes on hitting side of the wall, number of times. If I'm right, there cannot be a general formula...

Homework Statement Here is the question, which itself is rather confusing. A nonuniform surface charge lies in the yz plane. At the origin, the surface charge den- sity is 3.5 μC/m^2. Other charged objects are present as well. Just to the right of the origin, the electric field has only an x...

Hi to you all! I need your help with following problem: String with n characters is given. For each character in string there is probability p that it is wrong. Now you take a sliding window of length k, k<= n, that slides over that string. For the given parameters p,k and n one must must...

The derivation of the maxwell Boltzmann distribution involves maximizing the number of ways to obtain a particular macrostate with respect to how the particles are distributed in their respective energy states. One then arrives at $$\frac{n_i}{n} = \frac{1}{Z} e^{- \beta \epsilon_i},$$ where...

Hello all, How would I do this question by hand? I know I integrate from -infinity to +infinity for $f_x,y$, but I have no idea how to do it by hand! My algebra soup is bad, can someone please help me? P.S I heard some of my friends talking about some 'trick' you can do with the exponential...

What exactly prevents us from ruling out a uniform distribution on infinite sets? To be more precise, why are distributions and limits like \int_{-\infty}^{+\infty}dx\,\lim_{\sigma\to\infty}f_{\mu,\sigma}(x) = 1 \int_{-\infty}^{+\infty}dx\,\lim_{\Lambda\to\infty}\frac{1}{\Lambda} \chi_{[a,a+L]}...

How does the texture of a surface affect the concentration of charge on that surface? Say we compare a balloon (smooth) and a football (textured) (ignoring material differences) and give them the same total charge. Then we introduce dust particles. How do the two surfaces attract dust...

1. A harried passenger will miss by several minutes the scheduled 10 A.M. departure time of his fight to New York. Nevertheless, he might still make the flight, since boarding is always allowed until 10:10 A.M., and extended boarding is sometimes permitted as long as 20 minutes after that time...

The lecturer did not explain this for some reason. Assuming that we have a gass where all the particles have a certain absolute velocity v. Directions of v vector are random though, giving velocity vector a uniform direction distribution. That means that a velocity vector of any random...

Gammaray bursts (GRB) may affect the prevalence of life in various different regions of the galaxy. http://arxiv.org/abs/1409.2506 On the role of GRBs on life extinction in the Universe Tsvi Piran, Raul Jimenez (Submitted on 8 Sep 2014) As a copious source of gamma-rays, a nearby Galactic...

I accidentally posted this to the "Calculus & Beyond" forum when I meant to post it to the physics forum. If someone can tell me how to move this post, I will get rid of it here! Homework Statement Consider a property, for example temperature θ, that is conserved during advection (i.e. Dθ/Dt =...

Homework Statement A solid conducting sphere of radius 2.00 cm has a charge 16.00 µC. A conducting spherical shell of inner radius 4.00 cm and outer radius 5.00 cm is concentric with the solid sphere and has a total charge of -3.00 µC. (Take radially outward as the positive direction.) Find...

I've noticed that the vast majority of named or important mathematical constants, are what you might call small numbers. Their modulus lies very often in the range [0,5]. Here's two examples of tables: http://en.wikipedia.org/wiki/Mathematical_constant#Table_of_selected_mathematical_constants...

Residential DC power distribution, well that’s the end goal. The main question is about stepping down a 24v 4amp lead acid deep cycle battery bank to accommodate normal DC usage voltage. For example 24v 4amp too: 12v 1a, 5v 400ma, 9v .4a, 12v 2a. Was thinking of making adjustable outlets so...

I'm trying to interpret the expression of a microcanonical distribution for energy E_0 of a particle of mass m moving about a fixed centre to which it is attracted by a Coulomb potential, Zr^{-1}, where Z is negative. The function expression looks like this: ρ_{E_0}(\textbf{r,p}) = \delta(E_0...

what is the best software to calculate power losses in a distribution system?

Hi, I have never quite worked this type of probability question out, so would like some help please. Imagine this scenario: There are 4 people sat around a table, A, B, C and D. A is sitting opposite C, B is sitting opposite D. There is a bag with 16 balls numbered 1-16. The balls are...

The following problem is from "Probability and Statistics in Engineering - Hines, Montgomery" A potential customer enters an automobile dealership every hour. The probability of a salesperson concluding a transaction is 0.10. She is determined to keep working until she has sold three cars...

Hi, I understand that Volume of Distribution (Vd) = elimination constant (k) * Clearance (Cl), but I can't visualize why clearance would be proportional to volume of distribution. Can someone help explain this to me? I feel like it should be a more complicated relationship. Clearance = Mass...

Homework Statement i am having problem with part iv ) . the ans is 0.04519 . can anyone tell me how to do this ? i have solved part i , ii and iii ..p/s line 1: A tank contain 10^5 cm3 of water Homework Equations The Attempt at a Solution

Hi, I'm struggling to know what distribution this question requires, and what should be signalling the distribution type: A manufacturer claims at most 5% of his product will sustain fewer than 1000hrs of operation before needing service. Twenty products are selected at random from the...

Hi all, I am trying to describe/understand how to define a 2-plane distribution in R^3 , i.e., an assignment of a 2-plane at each tangent space, when the distribution is given in terms of the basis of a plane in (R^3, cylindrical). It has just been a while since I have worked with cylindrical...

Homework Statement A coffee shop sell tea and coffee. The number of cups of coffee sold in a minute can be assumed to be a random poisson variable with mean = 1.5 . The number of cups of tea sold can be assumed to be an independent random variable with mean = 0.5. Calculate the probablity...

I am trying to calculate the distribution of a number of units between two points with a desired average not necessarily in the middle. In an even distribution I would normally find the difference between the two points and use the result to divide the number of units for distribution. 100...

Homework Statement For the negative binomial distribution, with r known, describe the natural parameter space Homework Equations the pmf for the negative binomial distribution with parameters r and p can be 1) P(X=x|r,p)= \binom {x-1}{r-1}p^{r}(1-p)^{x-r} where x=r,r+1,... , or 2)...

Homework Statement Basically, I'm told that two insulated metal spheres, one positively charge (+20uc, sphere A) and one negatively charged (-10 uc, sphere B) come into direct contact (so obviously conduction is the method of charge), and that sphere A's radius is twice the size of sphere...

Homework Statement Hi! This is not really a problem. I'm just confused on how to express the charge distribution of a set of point charges in spherical coordinates. From our discussion, ρ(\vec{r})=\sum\limits_{i=1}^N q_i δ(\vec{r}-\vec{r}') where \vec{r} is the position of the point where...

"In multivariate probability distribution higher-order cumulants contain information of decreasing significance, unlike higher-order moments".

Force Distribution Hello, I have probably a fairly simple question about how force is distributed. If i were to have some type of setup where a hydraulic cylinder with a one inch rod was pushing down (say 50 lbs) onto a plate, or something of that sort, how would that force be distributed...

Hi there Can anyone tell what is the meaning of boundary conditions for temperature distribution in a flowing viscous fluid in a pipe ? for example I need some one explane for me this: T = T1 at r = R, x<0 T = T0 at x = 0, r<R where T1 is a temperature of well and T0 is a temperature...

Elecrical distrabution question if I may. I am not an EE and only an avid farmer with a nessesity for electrical knowlage. Here is my question. I am using two unlike transformers with the same values.( 5oKVA single phase 120/240-600V). Starting at the utility pole where I have 200amp 120/240V...

Given that the formula for spectral distribution of synchrotron radiation can be expressed in terms of a rapidly converging integral and graphed as a curved relationship between power radiated and the photon energy, is this curve considered a linear curve or a bell type curve or sinusoidal...

According to wiki: http://en.wikipedia.org/wiki/Poisson_process The probability for the waiting time to observe first arrival in a Poisson process P(T1>t)=exp(-lambda*t) But what is the Probability Distribution P(T1=t) of the waiting time itself? How to calculate that?

I thought I understood all the theory quite well and sat down to begin coding until I realized that calculating a probability at a point within a normal distribution in the application of bayes' rule you can't simply plug the point into the normal distribution and get the value since the...

Definition/Summary The exponential distribution is a probability distribution that describes a machine that it equally likely to fail at any given time. Equations f(t) = e^{-\lambda t} \lambda Extended explanation A machine is equally likely to fail at any given time. For any t...

Hi FWHM on a velocity distribution provides me with a specific velocity. What does FWHM say about the velocity distribution, I mean, does FWHM give me the most probable velocity of the distribution or something like that? Thanks

Okay, so I guess my first question is if the main utility of the normal distribution ##f(x)## is to provide a probability measure for any subspace of the measurable space ##(\mathbb{R},\mathcal{B})## (where ##\mathcal{B}## is the borel σ-algebra on the real numbers) by defining the measure as...