Poisson Definition and 441 Threads

1. Homework Statement During a typical Pennsylvania winter, I80 averages 1.6 potholes per 10 miles. A certain county is responsible for repairing potholes in a 30 mile stretch of the interstate. Let X denote the number of potholes the county will have to repair at the end of next winter. 1...

Homework Statement Telephone calls enter a college switchboard according to a Poisson process on the average of three calls every 4 minutes (i.e., at a rate of λ=0.75 per minute). Let W denote the waiting time in minutes until the second call. Compute P(W>1.5 minutes). Homework Equations...

I might need you guys to help me see how this proces, will be distributed: Suppose we have a large amount of elements N(≈1012). I'm simulating a system where I for each iteration damage a random element. If an element gets damaged its damagecounter goes up 1. So say I pick element number...

I'm studying Bio-statistics and I came across this problem from the textbook.It's actually answered on the back of the book, but I couldn't really get the same numbers. i Desease-free infants at the end of month i 0 2500 1 2425 2 2375 3 2300 4 2180 5 2000 6 1875 7 1700 8 1500 9...

Dear all, I have a problem in solving covariance of Bivariate Poisson Distribution Let X_i \sim POI (\theta_i) , i = 1,2,3 Consider X = X_1 + X_3 Y = X_2 + X_3 Then the joint probability function given : P(X = x, Y = y) = e^{\theta_1+\theta_2+\theta_3} \frac {\theta_1^x}{x!} \frac...

Homework Statement In a manufacturing process for electrical components, the probability of a finished component being defective is 0.012, independently of all others. Finished components are packed in boxes of 100. A box is acceptable if it contains not more than 1 defective component...

Homework Statement Use 1) \frac{1}{2\pi}\int\limits_{-\pi}^{\pi} \frac{r_0^2 - r^2}{r_0^2 - 2rr_0cos(\theta-t) + r^2} dt = 1 to compute the integral: 2) \int\limits_{-\pi}^{\pi} \left[1 - acos(x) \right]^{-1} dx for 0<a<1 [/itex]. The Attempt at a Solution I looked on Wolfram...

Homework Statement In New York in the last 3 years there were 55 driving accidents. Assume all days are alike. What is the approximate probability that "in the next 3 years there will be at least 2 days with more than one accident". Homework Equations Poisson approximation The...

Hello! I am trying to understand an example from my book that deals with two independent Poisson random variables X1 and X2 with parameters λ1 and λ2. The problem is to find the probability distribution of Y = X1 + X2. I am aware this can be done with the moment-generating function technique...

Hello, I'm reading a text about statistics, but I don't understand why Poisson applies. (Note, this is not an assignment or anything like that.) Why would X be Poisson distributed with that parameter theta? The only Poisson that I could find reasonable is modelling X as Poisson...

Are both sensible (equivalent? contradictory?) interpretations of "Poisson" behavior? I've come across two quite distinct notions (or so it seems to me, anyway) of Poisson behavior and I'm not sure if they're equally sensible or perhaps even equivalent. I'll apply both "views" to the same case...

Let me just head off the first waves of posts this thread will likely get. I am very fluent in quantum mechanics. I am completely aware of the behaviour of a commutator structure: simultaneous eigenbasis, etc. I understand how commutators model the structure that quantum mechanics has. My...

Homework Statement Can you look at Poisson's formula for a half plane as a limit case of Poisson's formula for a disk? http://en.wikipedia.org/wiki/Poisson_kernel I can find lots of information about the Poisson kernel for a disk, but not for the half plane. I do know on can mat the unit...

Homework Statement A hardwhere store sells on average 8 drills per week. The store receives ONE delivery of drills at the same time each week. Find the no. of drills that need to be in stock after a delivery for there to be at most a 5% chance of the store NOT having sufficent drills to meet...

Homework Statement Suppose that stress fractures appear in railway lines according to a Poisson process at a rate of 2 per month. a)Find the probability that the 4th stress fracture on the railway line occurred 3 months after the process of checking the new railway lines. b)Suppose new...

Hi, I am working on FEM methods as a part of my senior year project and I have written a poisson solver for the same purpose. The solver works pretty well on the simple problems that I have designed as of now and seems to give correct answer (i.e. the data matches the theoretical prediction) 1...

Homework Statement The rate of occurrence of events in a non-homogeneous Poisson process is given by: λ(t)=12t e-2t. (c) Find the p.d.f. of the time until the first event occurs after time t = 1. (e) After what time is it 95% certain that no further events will occur? Homework Equations...

Hello! I am writing because I recently became interested in probability distributions, and I have to you a few questions. Poisson distribution is given as a probability: f(k;\lambda)=\frac{\lambda^{k}e^{-\lambda}}{k!} But what is lambda? Suppose that we consider as an unrelated incident...

hello everybody. can we define a poisson ratio for fluids, eg for water?? if no, why? n if yes, how?? thnx.

how can i show that the Poisson distribution is properly normalized?

[SIZE="6"]SOLVED Homework Statement I am trying to prove that the poisson distribution is normalized, I think I've got an ok start but just having trouble with the next step. Homework Equations A counting experiment where the probability of observing n events (0≤n<∞) is...

Homework Statement An insurer uses the Poisson distribution with mean 4 as the model for the number of warranty claims per month on a particular product. Each warranty claim results in a payment of 2 by the insurer. Find the probability that the total payment by the insurer in a given...

Homework Statement Imagine you want to go from A to C via B. So you have two steps: A to B and B to C. Let's assume the time taken (t1) to go from A to B is Poisson and is given by Pab(t1) and the for B to C is t2 and the distribution is Pbc(t2). You are given: Pab(t1) = k1exp(-k1t1) and...

Homework Statement Imagine you want to go from A to C via B. So you have two steps: A to B and B to C. Let's assume the time taken (t1) to go from A to B is Poisson and is given by Pab(t1) and the for B to C is t2 and the distribution is Pbc(t2). You are given: Pab(t1) = k1exp(-k1t1) and...

I am in an error analysis class and our homework has asked us this (we will be writing a computer program to do this): "Create a sample with 396 draws from a Poisson distribution with N=1000 and 4 draws from the uniform distribution between 0 and 105. This sample represents data from a CCD...

Hello, Quick question on how you would go about calculating this. A grade of steel has the following properties; Tensile strength = 300 N/mm^2 - (not relevant?) Youngs Modulus = 200 GPa Poisson Ratio = 0.3 The grade of steel is 2m long, with a 20mm cross sectional area. It is positioned...

Homework Statement For a particle, calculate Poisson brackets formed by: 1)The Cartesian components of the linear momentum \vec p and the angular momentum [/itex]\vec M =\vec r \times \vec p[/itex]. 2)The Cartesian components of the angular momentum.Homework Equations [u,p]_{q,p}= \sum _k...

These three quotes talk about the use of the Poisson and normal distributions as approximations for the binomial when n is large. The first two quotes here say Poisson is best when p small, and the normal otherwise. The third seems to change the story; it says Poisson is best for large p too. Is...

Olbers' paradox states that if the universe is infinite, static and homogeneous then why is the night sky dark. Of course it's been resolved but it brings up an interesting probability question: If we model the universe with a spatial Poisson model (probability that a small element is...

Homework Statement Homework Statement A particle detector is set up to detect type A particles. These are detected as a poisson process with parameter lamda = 0.5 per day. (i) What is the probability that 3 or more will be detected in anyone day? (ii) What is the distribution of...

The following problem came up in my work. You have a tube, open at the top. Raindrops fall into the mouth of the tube at a mean rate i per second, 0 <= i < 1, in a Poisson process. There's a hole in the bottom of the tube. When there's water in the tube, it flows out at a constant rate of 1...

Given a poisson process Z(t) with a given rate lamda, k and m nonnegative integers and t and c real and positive numbers, calculate the probability: P(Z(t-c)=m | Z(t)=k) thanks

I need help with aPoisson distribution problem please. Question is: company capable of handling 5 calls every 10 min on new system. Prior to new system, company analysts determined incoming calls to the system are Poisson distributed w/ a mean equal to 2 every 10 min. what is the probability...

Hi, I am stumped by how to expand/prove the following identity, \{L_i ,L_j\}=\epsilon_{ijk} L_k I am feeling that my knowledge on how to manipulate the Levi-Civita is not up to scratch. Am i correct in assuming, L_i=\epsilon_{ijk} r_j p_k L_j=\epsilon_{jki} r_k p_i Which...

Hello, I am trying to find a characteristic function (CF) of a Compound Poisson Process (CPP) and I am stuck :(. I have a CPP defined as X(t) = SIGMA[from j=1 to Nt]{Yj}. Yj's are independent and are Normally distributed. So, in trying to find the CF of X I do the following: (Notation...

Homework Statement How to find for a Poisson distribution the number of successes for a given probability and mean. For example, for mean, \lambda, of 1, and a required probability of 0.01, what would the number of successes in the time interval be?Homework Equations...

Homework Statement question A ciclindrical metal specimen 10 mm in diameter is stressed elastically in tension. A force of 15000 N produces a reduction in diameter of 0.007 mm. Compute Poisson ratio if its elastic modulus is 100 GPa Homework Equations E=stress/strain The...

question A ciclindrical metal specimen 10 mm in diameter is stressed elastically in tension. A force of 15000 N produces a reduction in diameter of 0.007 mm. Compute Poisson ratio if its elastic modulus is 100 GPa my attempt D original = 0.01m change in D = 0.000007m F=15000N E=...

This isn't actually a homework problem, but a problem from a book, but as it's quite like a homework problem I thought this forum was probably the best place for it. Homework Statement Consider a system with one degree of freedom, described by the Hamiltonian formulation of classical...

Homework Statement If X is a Poisson random variable with \lambda = 2 find the probability that X>0.5. Homework Equations The Poisson PDF: P(x,\lambda) = \frac{\lambda^k}{k!}e^{-\lambda} The Attempt at a Solution Usually with these sorts of probability problems where they ask...

Homework Statement [/b] There are two problems I need help with, which are posted below. Any help is appreciated. 1)Let X have a Poisson distribution with parameter λ. If we know that P(X = 1|X ≤ 1) = 0.8, then what is the expectation and variance of X? 2)A random variable X is a sum of...

Homework Statement The number of sales made by a used car salesman, per day, is a Poisson random variable with parameter \lambda. Given a random sample of the number of sales he made on n days, what is the most powerful test of the hypothesis Ho: p = 0.10 versus Ha: p = 0.25, where p is the...

The number of cars driving past a parking area in a one-minute time interval has a Poisson distribution with mean lambda. The probability that any individual driver actually wants to park his or her car is p. Assume that individuals decide whether to park independently of one another. a)If one...

Homework Statement In one of the archaeological excavation sites, the artifact density (number of prehistoric artifacts per 10 liters of sediment) was 1.0. Suppose you are going to dig up and examine 50 liters of sediment at this site. Let r = 0, 1, 2, 3,… be a random variable that represents...

Homework Statement A trial consists of tossing two dice. The result is counted as successful if the sum of the outcomes is 12. What is the probability that the number of successes in 36 such trials is greater than one? What is this probability if we approximate its value using the Poisson...

Homework Statement A casino slot machine costs C dollars per play. On each play, it generates random variable X ~ Poisson with parameter λ < 1, and pays the player X! (X factorial) dollars. As a function of the fixed parameters λ and C, how much money would you expect to win (or lose) per turn...

I am trying to use Gaussian elimination to solve the 2D poisson equation. I've done this for the 1D problem without problems, but for some reason my solution for the 2D problem is incorrect; it looks something like the correct solution but it's as if the resulting field were cut in half, so...

The explanation for the Poisson distribution in reference book is " when given an interval of real number, assume events occur at random throughout the interval. If the interval can be partitioned into subintervals of small enough length such that 1. the probability of more than 1 event in a...

Hi Guys, I've used this forum as a great resource for a while now and it's always helped me out. Now I'm really stuck on something and was hoping you guys could help out. It's a pretty long question, but if you guys can just give me a general direction of what to do, I can go ahead and work it...

Dear All, The bivariate Poisson distribution is as follows, \[ f(y_{s},y_{t})=e^{-(\theta_{s} + \theta_{t}+\theta_{st})}\frac{\theta_{s}^{y_{s}}}{y_{s}!}\frac{\theta_{t}^{y_{t}}}{y_{t}!} \sum_{k=0}^{min(y_{s},y_{t})} \binom{y_{s}}{k} \binom{y_{t}}{k}...