Poisson Definition and 509 Threads

A store opens at 8 in the morning. from 8 until 10 customers arrive at poisson rate 6 per hour. Between 10 and 12 they arrive at a poisson rate of 10 per hour. From 12 to 2, the store closes for lunch, Finally from 2 to 5 the arrival rate drops linearly from 10 per hour at 2 to four per hour at...

i am searching for a detailed discussion on the relativistic poisson brackets. where i can found it?

Homework Statement Given that \nabla2 1/r = -4\pi\delta3(r) show that the solution to the Poisson equation \nabla2\Phi = -(\rho(r)/\epsilon) can be written: \Phi(r) = (1/4\pi\epsilon) \int d3r' (\rho(r') / |r - r'|) Homework Equations The Attempt at a Solution I know...

Theorem: Let {N(t): t≥0} be a Poisson process of rate λ. Suppose we are given that for a fixed t, N(t)=n. Let Ti be the time of the ith event, i=1,2,...n. Then the (conditional) density function of Tn given that N(t)=n is the exactly the same as the density function of X(1)=min{X1,X2,...,Xn}...

Let {N(t): t≥0} be a Poisson process of rate λ. We are given that for a fixed t, N(t)=n. Let Ti be the time of the ith event, i=1,2,...,n. Then the event {T1≤t1, T2≤t2,...,Tn≤tn, and N(t)=n} occurs if and only if exactly one event occurs in each of the intervals [0,t1], (t1,t2]...

I have a Poisson-based question that I am not sure how to approach and solve. A processor receives groups of bits with a Poisson arrival rate of L. The probability of an error in receiving an erroneous bit is p. The number of bits in a group of bits is Poisson with mean M. If there is no error...

Hi all, I've taken a two-course undergrad QM sequence and have been reading Shankar's Principles of Quantum Mechanics. There is some reference to the similarity between the Poisson bracket in Hamiltonian mechanics and the commutator in QM. E.g. \{x, p\} = 1 (PB) [x, p] = i \hbar...

Social Properties and First order Links I wasn't sure to put this in the math or sociology form but I already have two Social Networks topics posted in the Math forum and I think I would like to devote more specific topics to the math forum. You are subscribed to this thread Erdős–Rényi...

Hi, all, Let's say we deploy some random points on a line of finite length according to a poisson distribution of density \lambda. Can I say that these points are also "uniformly" distributed on the same line? thks

I have an excel spreadsheet that uses poisson to figure out the probability of correct scores in soccer matches. How do I amend the spreadsheet to use a bivariate poisson distribution?

(Not sure if I should have posted this in the h/w problem section since it's not really hw...just a problem I've faced recently. But if it should be there, I can move it there. ) There are 5 boxes. Each box may contain a certain amount of marbles (1, 2, 3 etc.) and some have no marbles at...

The children in a small town own slingshots. In a recent contest 4% of them were such poor shots that they did not hit the target even once in 100 shots. If the number of times a randomly selected child has hit the target is approximately a Poisson random variable, determine the percentage of...

Poisson RP: MLE of "k" P(n,tau) = [ [ (k*tau)^n ] / n! ] * exp(-k*tau) Parameter k is the process of an unknown non random variable that I want to estimate. I have determined that k^ML = [1 / (n*tau) ] sigma (xi) I believe this is correct... How do I determine if K^ML is biased?

Homework Statement Hi, I am looking for a hint, how to solve the following Dirichlet problem. All the standard textbooks have only examples for Dirichlet problems in rectangular or polar coordinate systems, but this problem is defined for a parabolic region. Homework Equations uxx+uyy=2...

Please how would one derive the Poisson Equation model, \nabla^{2}\psi(x) = \frac{F(x)}{T}, for Transverse displacement \psi(x) of a stretched string under constant non-zero tension T and an externally applied transverse force F(x) . Assuming small angle with the horizontal (i.e...

Hello I am trying to build a 3D Poisson solver using method of moments. I need to find out the Green's function for the system. My system is a rectangular box and boundary conditions are as follows: On all surfaces BC is neumann. Only on the upper and lower surface, the middle 1/3 region...

I need to fit a Poisson distribution to this set of data (no. of counts of radioactive decay) The number of counts in a fixed time interval was recorded 500 times. With the number of counts going from 0 - 9 respectively 39 106 130 100 67 34 15 7 1 1 I understand how to use...

Please help with this thanks :) 1. (a) Define the Poisson probability distribution with mean μ. (b) Write down the binomial distribution for x successes in n independent trials each with probability p of success. (c) On average, 0.15% of the nails manufactured at a factory are known to...

Hi I am working with MOSFETs and in this context I am trying to solve poissons equation inside a MOSFET. Only in the direction from the gate through the oxide and into the silicon. I know the analytic solution but now I want solve Poissons equation with the use of finite difference...

Homework Statement A source of liquid is known to contain bacteria, with the mean number of bacteria per cubic centimeter equal to 3. Ten 1 c.c. test tubes are filled with liquid. Calculate the probability that all 10 test tubes will show growth, that is contain at least 1 bacterium each. (use...

Homework Statement Calculate the Poisson bracket [H, Lz] in Cartesian Coords. Transform your result to cylndrical coords to show that [H, Lz] = -dU/dphi (note: partial derivs), where U is the potential energy. Identify the equivalent result in the Lagrangian formulation Homework Equations...

b]1. Homework Statement [/b] prove that \sum( (e^(-u)) (u(^(x)) )/x! (from x=o to n ) = \int ( (e^(-y))(y^n) )dy/n! (from u to infinite ) Homework Equations The Attempt at a Solution i know that the left is Poisson distribution formula but how to do with the 'sum' ? and...

I had this problem on my last midterm and received no credit for these parts. 1. Express trains arrive at Hiawatha station according to a Poisson process at rate 4 per hour, and independent of this, Downtown local buses arrive according to a Poisson process at rate 8 per hour. a. Given that 10...

I have completed an experiment to measure the decay rate of an isotope, and I am trying to estimate uncertainties. The half life is 40 seconds, with decays counted over a 15 second period (with many of these 10 second periods for a total of 6 minutes of recordings) However in more detailed...

Hi all, I have a question about probability. Can you help me? There are 2 events: - Customer A arrives the system B in accordance with a Poisson process with rate Lambda1 - Customer A arrives the system C in accordance with a Poisson process with rate Lambda2. Given that Poisson...

Homework Statement Let N,X1, X2, ... be independant random bariables where ?N has a poission Distribution with mean 3 while X1, X2... each has a poisson distribution with mean 7 Determine E[N \sum^N_{i=1} X_i] Homework Equations The Attempt at a Solution E[N \sum^N_{i=1} X_i]...

Homework Statement In a Poisson process with intensity λ, let X1 be the time until the first event and let X2 be the time between the first and the second event. Let Y be the time until the second event, that is, Y = X1 + X2. Find the density function f(y). 2. The attempt at a solution...

Hi all, I have a probability problem. Can you help me? Thank you! Here is the problem: Consider the queueing system, there are n customers 1, 2, ...N. Customer 1 arrives in accordance with a Poisson process with rate Lamda, customer 2 arrives in accordance with a Poisson process with rate...

Am just playing around, and following examples of Fourier transform solutions of the heat equation, tried the same thing for the electrostatics Poisson equation \nabla^2 \phi &= -\rho/\epsilon_0 \\ With Fourier transform pairs \begin{align*} \hat{f}(\mathbf{k}) &= \frac{1}{(\sqrt{2\pi})^3}...

Homework Statement An actuary has discovered that policyholders are three times as likely to file two claims as to file four claims. If the number of claims filed has a Poisson distribution, what is the variance of the number of claims filed? [b]2. Homework Equations [/]...

Homework Statement Let X\sim Poi(\lambda) and assume \lambda\sim Uni(0,5) Q: Find \mathbb{P}\{X \geq 3\}Homework Equations For a Poisson r.v. with parameter lambda, \mathbb{P}\{X = k\}=\frac{\lambda^{k}e^{-\lambda}}{k!} and the probability that lambda is in the interval (0,5) is 1/5 and 0...

Hi, I have a (maybe rather technical) question about the Hamiltonian formulation of gauge theories, which I don't get. With an infinitesimal symmetry on your space-time M one can look at the corresponding transformation of the canonical variables in phase-space PS. This can be done by a phase...

Hello everybody I've been searching this today but I am a bit lost now. I've encountered two forms of Gauss law in its differential form, Poisson equation : del2V(r) = -p(r)/e del2V(r) = -4*pi*p(r)/e where V:e.potential, p:charge density, e:permivity Now, what's the difference...

Homework Statement Suppose a typographical errors committed by a typesetter occurs randomly. If that a book of 600 pages contains 600 such errors, calculate the probability by using Poisson's distribution. i) that a page contains no errors ii) that a page contains at least three errors...

Hi Homework Statement Verify, that u(\vec{x}) := - \frac{1}{2 \pi} \int \limits_{\mathbb{R}^2} \log ||\vec{x} - \vec{y} || f(\vec{y}) d \vec{y} is the general solution of the 2 dimensional Poisson equation: \Delta u = - f where f \in C^2_c(\mathbb{R}^2) is...

In many book I read, problems for electrostatic potential always lead to solving Poisson equation. I saw a problem about a spherical shell carrying some amount of charges uniformly on the surface with density \rho, and then someone put a small patch on the sphere. The patch is then made a...

Hello guru's, I've been trying to figure out a way to incorporate an electric field source in the Helmholtz equation, and have been accumulating lots of question marks in my head. So in case of no static charge, \nabla^{2} E - \mu (\epsilon\frac{d^{2}}{dt^{2}} + \sigma\frac{d}{dt}) E = 0...

This is a general question. When evaluating Poisson brackets, can we assume that H = p^2/2m + V?

Hey guys, Can anyone please explain the differences between binomial and poisson distribution. THANK U>>>>>>>>>>>>>>>>>>>>>

Homework Statement If you find a mushroom, what is the chance that at least one more will be within one yard from it ? What is the chance that there is exactly one mushroom within the distance one yard from the point you stay? The mushrooms grow in a forest randomly , with density 0.5...

Homework Statement The number of customers entering a cafe during tea time is known to be poisson distribution with λ = 5. on a particular day, given that at least 2 customers have entered the cafe during the tea time. what is the probability that at least 1 more customers will enter the cafe...

[SOLVED] Poisson Distribution Homework Statement Let X be the number of people entering the ICU in a hospital. From Historical data, we know the average number of people entering ICU on any given day is 5 a) What is the probability that the number of people entering the ICU on any given...

Binomial, Poisson and Normal Probability distribution help! Hey everyone, I've just started a new section on probability (argh) in my math course, and unlike most other maths, I cannot cope! Anyway, I was wondering if anyone could tell me if I did the following question correctly! Any helps...

hello, I want to know that the poisson superfish code uses finite difrerence method or finite element method?

Homework Statement Suppose X has a Poisson distribution with parameter lambda. Given a random sample of n observations, Find the MLE of lambda, and hat lambda. Find the expected value and variance of hat lambda. Show that hat lambda is a consistent estimator of lambda. Homework...

Hi everyone, I have been trying to solve both laplace and poisson equation using method of separation of variable but is giving me a hard time. Pls can anyone refer me to any textbook that solve this problem in great detail? Thanks

Homework Statement Suppose that X has a poisson distribution with parameter \lambda . Given a random sample of n observations, find the MLE of \lambda , \hat{\lambda} . Homework Equations The MLE can be found by \Sigma^{n}_{i=1} \frac{e^{- \lambda} \lambda^{x_{i}}}{x_{i}!} = e^{-...

can anyone tell me why the poisson brackets for {x,p} = 1 ..from (dx/dx)(dp/dp) - (dx/dp)(dp/dx)... shouldn this equal 0??

Suppose \phi is a scalar function: R^n\to R, and it satisfies the Poisson equation: \nabla^2 \phi=-\dfrac{\rho}{\varepsilon_0} Now I want to calculate the following integral: \int \phi \nabla^2 \phi \,dV So using Greens first identity I get: \int \phi \nabla^2 \phi \,dV = \oint_S \phi...

Homework Statement Phone calls are received at Diane residence have a Poisson distribution with \lambda =2. a) If Diane takes a shower for 10 min, what is the probability that the phone rings Once or Twice. b) How long can she shower if the probability of receiving no calls be at most 0.5...