Poisson Definition and 509 Threads

Hey I have some problems understanding my statistics homework. I am given a data set giving the number of calls arriving to different switchboards in three hours as well as the total phone call duration in minutes for each switch board. Something like i y_i t_i -------------- 1...

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?

In 2003, there were many media reports about the number of shark attacks. At the end of the year, there were a total of 30 unprovoked shark attacks. By comparison, there were 246 shark attacks over the prior ten years. (a) Give an expression for the probability of more than 30 shark attacks...

Hi everyone, I am trying to solve this problem but I am stuck with doubts. Here are my ideas. Homework Statement Busloads of customers arrive at an infinite server queue at a Poisson rate λ Let G denote the service distribution. A bus contains j customers with probability aj = 1...

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 given by...

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 A store selling newspapers orders n = 4 of a certain newspaper because the manager does not get many calls for that publication. If the number of requests per day follows a Poisson distribution with mean 3, what is the expected value of the number sold? Homework Equations...

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...

Homework Statement Let N(t) be a Poisson process with intensity a. Let T be the occurrence of the first event in (0,t] for some t>0, if there is such a one. If there are no events in (0,t] we set T=t. Compute E(T). Homework Equations None. The Attempt at a Solution I have no clue...

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=...

[b]1. The distribution of flaws along the length of an artificial fibre follows a Poisson process, and the number of flaws in a length L is Po(L\theta ). Very little is known about \theta. The number of flaws in five fibres of lengths 10, 15, 25, 30 and 40 metres were found to be 3, 2, 7, 6, 10...

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...

Hey All, Can someone please explain to me the difference between a Poisson Process and a Renewal Process ? is it just that the Holding times for Poisson processes are exponential and Holding times for Renewal Processes are any kind of probability distribution (as the wiki page seems to imply)...

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}...

When considering the solution u(x,y) of the poisson equation u_xx + u_yy = -1 for (x,y) in G on a 2-dimensional domain G with Dirichlet boundary conditions u = 0 for (x,y) on boundary of G I am wondering the following: for what shape of the domain G do I obtain the largest area-average...

Homework Statement I am solving a particular probability question using Poission distributin after the Solving I get an equation Homework Equations 1.67 = e^-a (1/1-a) I ought to get the value of a from the equation but I was Unable to go further from here . The Attempt at a...

Suppose X and Y are independent Poisson random variables, each with mean 1, obtain i) P(X+Y)=4 ii)E[(X+Y)^2] I m trying to solve this problem but have difficulty starting ... If some one could give me a some pointers

Question: If X and Y are independent poisson variates with mean λ1 and λ2 respectively, what is the probability that i) X + Y =k ii) X = Y Solution: Dont know how to solve this .

Poisson errors for the distribution of galaxies?? Hi, I have some data regarding the distribution of galaxies of varying mass in different density regions of the Universe, from which I have a mass functions for each region. I would now like to introduce some errors so I can determine whether...

How can I prove that P( there exist a t>0 : the changeP_t is not in {0,1} ) = 0 where (P_t)_t>0 is a piosson Proces with parameter lambda > 0. Thank you.

Hi... Hope i 'll get the good result that where we practically use the binomial and poisson distribution in the field of engineering...

Homework Statement How do I evaluate this Poisson distribution? Homework Equations The Attempt at a Solution So I have figured out what the values for lambda and x are, but I don't know how to evaluate once I plug the values into the formula. λ = 20 x = 18 = [ e^-20...

Homework Statement A radioactive source emits particles according to a Poisson process, at an average rate of λ per unit time. Each particle emitted has probability p of being detected by an instrument, independently of other particles. Let X be the number of particlese emitted in a given...

I'm studying the Poisson Process (rate R) and I'm hung up on the issue of dependence. This seems like and easy question but I have no background in probability whatsoever. By definition, the number of events in disjunction time intervals are independent. Okay. Fine. But say we have an...

So my book merely mentions that this holds as a result of the central limit theorem for values of lambda greater than 10, but ideally greater than 32. Anyway I was wondering if anyone knew this actual proof as I am interested in seeing it step by step and I could not have found it anywhere...