Gaussian Definition and 706 Threads

Are there any sets of numbers that represent numbers of sets? Any sets of numbers that follow a Gaussian (normal) distribution?

Hi, I've got the right answer in this problem, but I'm not sure if I've got the correct reasoning Homework Statement A Gaussian wave packet travels through free space. Which of the following statements about the packet are correct for all such wave packets? I. The average momentum...

Homework Statement I need to have the Fourier transform of a Gaussian Homework Equations The Attempt at a Solution ∫(exp[-ax^2])(exp[-ikπx]) dx I tried by braking the last exponential into sine and cosine terms.The sine term is odd and it cancels.Then,I cannot evaluate the...

For the following Eo is epsillon zero Homework Statement 41. A solid nonconducting spere of radius R has a uniform charge distribution of volume charge density p = kr/R where k is constant and r is the distance from the center. Show the (a) the total charge on the sphere is Q =...

Can any resources on gaussian geometry be found on line?

Question: solve by using gaussian elimination: 3x - y + z = 1 2x + 2y – 5z = 0 5x + y – 4z = 7 what i did: step 1: new row 1 = old row 1 – row 2, I got: x – 3y + 6z = 1 2x + 2y – 5z = 0 5x + y – 4z = 7 step 2: new row 2 = old row 2 – (2 * row1) and new row 3 = old row 3 –...

I can't figure out how to get started on this problem. Maybe you guys can help. A spherical balloon carries a total cahrge Q(1C) uniformly distributed over the surface. At t=0, r=r(sub 0), at t=30s, r=2r(sub 0). Find what is the electron field at 90 s at a distance of .5m from the balloon...

What are Gaussian Normal Coordinates?

Hi, can anyone help me ? I want code (program) to solve Gaussian Elemination by C++ . Please Help me and I will really appreciate your time and effort in helping me in my assignment. Thanks.

Enter Here!? Hi, can anyone help me ? I want code (program) to solve Gaussian Elemination by C++ . Please :cry: :cry: very important:cry:

The question says show that the average value of k is k_0 for the function A(k)=\frac{1}{\sqrt{2\pi}a}e^{\frac{-(k-k_0)^2}{2a^2}. I know that this is a gaussian function and that the center is k0 but i am not sure how to show this is the average value of k, what equation for average value...

Hello,.. that's part of a problem i find in QFT (i won't explain it since it can be very tedious), the question is that i must evaluate the Multi-dimensional Gaussian Integral. \int_{-\infty}^{\infty}d^{n}V exp(x^{T}Ax)exp(ag(x)) for n\rightarrow \infty of course if the integral is...

Can you direct me to any websites or papers on how to solve these? We've been coming across them in Physics III, and I really want to know how to solve them. lol, It's getting annoying not knowing how to solve them or differential equations (finally taking it next semester).

Hi, I'm trying to evaluate the standard Gaussian integral \int_{-\infty}^{\infty} e^{-x^2} dx = \sqrt{\pi} The standard method seems to be by i)squaring the integral, ii)then by setting the product of the two integrals equal to the iterated integral constructed by composing the two...

check whether this result of this problem is consistent with this statement \vec{E_{above}} - \vec{E_{below}} = \frac{\sigma}{\epsilon_{0}} \hat{n} an infinite plan carries a uniform surface charge sigma. Find its electric field Solution: Draw a Gaussian Pillbox extending above and below the...

I have three sets of data that I’ve used to create three Gaussian distributions which have different means and standard deviations. The data sets are also correlated as the data is dependent on time. I want to compare the sum of two distributions with the sum of three distributions to find which...

I just realized that I accidentally didn't post this in the homework help section...if any mods can move this, I'd appreciate it. Sorry for the trouble! Hello. I need help solving the following problem: Consider a spherical Gaussian surface and three charges: q1 = 1.60 μC, q2 = -2.26 μC, and...

I was reading about the derivation of the Heisenberg Uncertainty Principle and how Heisenberg used Gaussian Distributions to represent the uncertainty of position and momentum in his calculation. Why is it that Gaussian Distributions were used? There are many different types of distributions...

I am doing a Gaussian Beam Optics Experiment - where I observe how lasers have a gaussian intensity profile. I've measured the beam radius at several points from the Laser in the far-field (ie. position 'z' >> Rayleigh Range). I want to know why is there a beam waist inside the laser. How...

Hi i need a good math site (easy to read) so i can find the gaussian distribution

hi I have problems with gaussian surface.:cry: is anybody who tell me here?:shy: help me please,thanks :-p

Hello everyone, I got stuck on a probability question and would be very thankful if someone could give me a hint: An Opaque bag contains 10 green counters and 20 red. One couner is selected at random and then replaced: green scores 1 and red scores zero. 1) Calculate the probability of...

I’m generating a 1 kHz square wave and adding Guassian noise to obtain a SNR of 0 dB (using Matlab6.5). The task is to design a filter that will filter out as much noise as possible from the square wave plus noise signal. The sampling frequency is 100kHz. Noise signal: 100.0*randn(1...

Evaluate: \frac{1}{\sqrt{2\pi} \sigma} \int_{-\infty}^{\infty} \, dx \, exp\left[-\frac{(x - \mu)^2}{2\sigma^2}\right] \, , where $\mu$ and $\sigma$ are complex numbers. I tried writing \begin{align} \sigma &= s_1 + is_2 \,\\ \mu &= m_1 + i m_2 \, . \end{align} The integral...

use gaussian elimination to solve the following system of equation: 2x + y - 3z = 3 4x - y + 2z = 25 -3x + 2y + 4z = -9 ok so first i rearranged them so the inital numbers were in decending order (for the pivot) R1 -> 4x - y + 2z = 25 R2 -> -3x + 2y + 4z = -9 R3 -> 2x + y - 3z = 3...

In academics, you hear so much about the Gaussian function, whether it be in statistics, physics, or even social sciences! The Gaussian function takes the general form of: f(x) = Ae^\frac{-(x-b)^2}{c^2} Further yet, the antiderivative of this function is the famous error function...

Anyone care to explain the concept of gaussian quatrature? I've tried some websites but they're a little over my head. An example would be appreciated, thanks!

S = Columns 1 through 3 1.0000 0 0 0 1.0000 0 0 0 1.0000 Columns 4 through 5 0.2750 -0.2786 -0.1750 0.5929 0.2250 0.1357 Which is the rref of A = 2 9 9 1 6 2...

I am looking for help with the following integral A = \int dx \int dy \exp(-a (x+y)^2 +ib(x-y)) sinc(cx+dy) sinc(dx+cy) where sinc(x) =\sin(x) / x for x \neq 0 and sinc(0) = 1 (pls forgive my poor latex) Either in the indefinite form or with the upper/lower limits at...

2 1 1 | 4 -1 2 1 | 3 7 6 5 | 19 Need a little help please

Any help on this one would be greatly appreciated. Due to that I can't find much of a connection (due to lack of inconsistent set of linear equations), and the fact that I'm unable to explain it properly, can someone please help me? Here's the question: If a system of linear equations is...

I am trying to to the Gaussian integral using contour integration. What terrible mistake have I made. I = \int_{-\infty}^\infty \mathrm{e}^{-x^2} \mathrm{d}x I consider the following integral: \int_C \mathrm{e}^{-z^2} \mathrm{d}z where C is the half-circle (of infinite...

Does anyone have any references or pointers to the complete electromagnetic field of a "Gaussian Beam"? By Gaussian, I mean that for a beam propagating in the z direction, a cross-section of the beam in the x-yplane has |E| = k exp( -(x^2+y^2)/w^2 ) see for instance...

How to prove the output of Linear Filtering a Gaussian Process is still Gaussian? It has been stated in many books I read, but none of them actually prove it. One even stated that "The technical mechinery to prove this property is beyond the scope of this book..." By definition, a Gaussian...

Hey, I've been learning about gaussian integrals lately. And I'm now stuck in one part. I am now trying to derive some kind of general formula for gaussian integrals \int x^n e^{-\alpha x^2} for the case where n is even. So they ask me to evaluate the special case n=0 and alpha=1. So its...

How do you show that a linear combination of two Gaussian Random Variables is again Gaussian?

28. The problem is stated as: A long, thin wire carrying 5.6nC/m runs down the center of a long, thin-walled, hollow pipe with radius 1.0cm carrying -4.2nC/m spread uniformly over its surface. (a)Find the electric field 0.50 cm from the wire. (b)Find the electric field 1.5 cm from the wire...

I tried to solve this Gaussian elimination algorithm problem (matrices) but for some reason when I plug in the x variables it doesn't work. The problem is: Alright so the first thing I did was divide the 1st row by 1/3 (scaling). Then I made the entries below the first pivot equal to 0...

I tried to solve this Gaussian elimination algorithm problem (matrices) but for some reason when I plug in the x variables it doesn't work. The problem is: Alright so the first thing I did was divide the 1st row by 1/3 (scaling). Then I made the entries below the first pivot equal to 0...

I am not sure how to solve this: Given an augmented matrix, find conditions on a, b, c for which the system has solutions: -1 -2 3 b -1 -6 23 c -3 2 4 a so by Gaussian elimination, the matrix I ended up with is 1 2 -3 -b 0 4 -20 b-c 0 0 -35...

Hi. Suppose I have a function T(x,t), units are in Kelvins. I then do a convolution with a gaussian G(t), and the result is also in Kelvins. What are the units of the gaussian G(t)? Thanks.

I need a math guru to explain why and how the elimination method of solving simultaneous equations works ? why do we add or subtract the two equations ?(I undertand in order to eradicate either term) but I need to know from the basics . For that matter, how/why does the substitution method...

Derive \frac{n_1}{s_o} + \frac{n_2}{s_i} = \frac{n_2-n_1}{R} for Gaussian optics from the following equation \frac{n_1}{l_o} + \frac{n_2}{l_i} = \frac{1}{R} \left( \frac{n_2s_i}{l_i} - \frac{n_1 s_o}{l_o} \right) by approximating l_o = \sqrt{R^2 + \left( s_o + R \right) ^2 -...

I am looking for a mathematical equation which is similar to the Gaussian normal distribution curve, but I need one which terminates at a finite x = X and not at infinity, ie, f(x \geq X) = 0, but, f(x \leq X) = a function which has a Gaussian shape-like curve. Is there one such as this that...

Hi All, I am just wondering whether there is any kind soul to help me out with the following problem: If a gaussian beam is truncated by the circular aperture situated at the beam waist just before the entrance of a microscope objective lens, what should be the intensity distribution of...

Construct a spherical gaussian surface centered on an infinite line of charge. Calculate the flux through the sphere and thereby show that it satisfies gauss law. I know how i can do it for a cylinder, but a sphere? I know that the ends of the wire (one diameter) wil have zero flux at it's...

\psi (x)= \frac{1}{(\pi\Delta^2)^\frac{1}{4}} e^(\frac{i<p>(x-<x>)}{\hbar})e^(\frac{-(x-<x>)^2}{2\Delta^2}) as \Delta\rightarrow\infty should approach the plane wave \frac{1}{(2\pi\hbar)^\frac{1}{2}} e^(\frac{i<p>x}{\hbar}) up to a phase factor. I guess this happens by setting the...

So here is an example of what I am trying to do. We know that div of an E field=p/eo where p=charge density and eo=the permittivity of free space. This equation is expressed in MKSA units. In order to convert this into Gaussian units, we must multiply E by 1/sqare root of 4*pi*eo, and...

Hi, Need help desperately! I am trying to figure out the area under a gaussian cone by finding the integral of 2PIArEXP[-(r^2)/(2sigma^2)] dr My supervisor thought it is 2PI [A sigma^2 EXP(-(r^2)/(2 sigma^2)] Between 0 and infinity and he came up with the...

A small copper spherical BB of radius a is located at the center of a larer hollow copper spherical shell of inner radius b and outer radius R. A charge of +q is on the small BB. The hollow copper shell has zero charge on it. a) What is the electric field within the BB (for radii r<a)? b)...