Poisson Definition and 509 Threads

For a magnetostatics problem I seek the solution to the following equation \frac{1}{x}\frac{d}{dx} \left( x \frac{dy(x)}{dx} \right) = -C^2 y(x) (C a real constant) or equivalently x \frac{d^2 y(x)}{dx^2} + \frac{dy(x)}{dx} + C^2 x y(x)=0 It seems so simple, but finding a...

Let {Mi(t), t >= 0 }, i=1, 2 be independent Poisson processes with respective rates λi, i=1, 2, and set N1(t) = M1(t) + M2(t), N2(t) = M2(t) + M3(t) The stochastic process {(N1(t), N2(t)), t >= 0} is called a bivariate Poisson process. (a) Find P{N1(t) = n, N2(t) = m} (b) Find Cov...

Homework Statement Let {Mi(t), t >= 0 }, i=1, 2 be independent Poisson processes with respective rates λi, i=1, 2, and set N1(t) = M1(t) + M2(t), N2(t) = M2(t) + M3(t) The stochastic process {(N1(t), N2(t)), t >= 0} is called a bivariate Poisson process. (a) Find P{N1(t) = n...

Homework Statement Cars pass a certain street location according to a Poisson process with rate lambda. A woman who wants to cross the street at that location wait until she can see that no cars will come by in the next T time units. Find the probability that her waiting time is T...

Homework Statement numerical solution of poisson equation with application to the pumping of water from drains 1. time 2. Amount of water has been pumped Homework Equations The poisson equation The Attempt at a Solution 1. I know i have to use iteration 2. I am still...

Hello, From the following formula in the following theorem I am to deduce the mean delay of a customer arriving at a queue. Theorem 1 Suppose that customers arrive at a single server queue according to a Poisson process mean rate q and that service times are exponentially distributed mean...

I want to test if one Poisson distributed result a is large than another one b. I don't know much about statistics, but I understood the Wiki article about testing normal distribution however they need the number of samples there. Basically I measure two Poisson distributed variables, I get two...

I'm not sure how to get started with this: Suppose you have two independent poisson processes, X ~ Po(Lambda1) Y ~Po (Lambda2). How would you figure out the probability of one coming before the other? Thanks

Why does particle emission follow a poisson? Thanks in advance

Here I have a translation from French to English of the original paper by Poisson about his brackets. I cannot understand why the function a=f(q,u,t) doesn't have a second order derivative (in q or u). The problem is on the top of the third page (second .JPG) after he took the time derivative...

Homework Statement I'm trying to understand the poisson to normal approximation. I've got this book that says the poisson distribution approximates the normal distribution well when the mean is greater than 100. 2. understanding/interpretation Let's call N the number of counts observed...

[SOLVED] A Chebyshev interval with a poisson distribution Geophysicists determine the age of a zircon by counting the number of uranium fission tracks on a polished surface; the number of these uranium fission tracks on this surface follows a Possion distribution. A particular zircon is of...

Doing Physics at University and I have never done poisson distributions. How the hell do I do it? The question is... Show that the data on the number of cavalry deaths in the Prussian Army in the 19th Century are consistent with the poisson probability distribution. The date were accumulated...

Homework Statement An ailrine always overbooks if possible. A particular plane ha 95 seats on a flight in which a ticket sells for $300. The airline sells 100 such tickets for this flight. Use a Poisson approximation only. (a) If the probbility of an individual not showing is...

Homework Statement Consider a 1D sample, such that for x < xb the semiconductor has a dielectric constant \varepsilon_{1}, and for x > xb has a dielectric constant \varepsilon_{2}. At the interface between the two semiconductor matierials (x = xb) there are no interface charges. Starting...

[SOLVED] Poisson brackets. Homework Statement Show that, if Poisson brackets (g,h) = 1, then (g^{n},h) = ng^{n-1} where g = g(p,q) and h = h(p,q) p and q are canonical coordinates The Attempt at a Solution I suppose that this is purely mathematical, but I am still searching for a detailed...

[SOLVED] Bernoulli, Poisson &amp; Normal Probability Homework Statement Every chocolate bar contains 100 squares, with 10% of the individual squares presenting a health hazard to people consuming them. (a) Using the Binomial, Poisson and Normal distributions, write down formulas for...

We have to show that [Lx,Ly] = Lz [Ly,Lx] = -Lz [Lx,Lx] = 0 and I have done this. We then need to comment on the significance of these results, which I'm not sure of. I know in QM you get similar results for commutators of these quantities, and it means that you can't simultaneously know...

Can someone help me with this question: If X has a Poisson distribution so that 3P(X=1)=P(X=2) find the pdf of X, and P(X=4)?

I have 2 dependent random Poisson distributed variables, X and Y. I have that E[X] = mu and E[Y] = c*mu where c is just a constant. Now I'm trying to get the joint distribution of XY. I've found the expression of the bivariate Poisson distribution but the problem is in order to use it I have...

1. Of what type is Poisson’s equation uxx + uyy = f(x,y) ? I used that if you have auxx+buxy+cuyy+dux+euy +fu+g=0 where a, b, c, d, e, f, g is constants, and if b^2-4ac<0 then you get an elliptic type because b=0, a=1, c=1 gives 0^2-4*1*1=-4<0 => elliptic Is this right? And why...

Hi, I have This probability problem and I don't know how to do it: A company makes plastic panel used in automobiles. The panel production process is such thast the number of flaws on a panel follows a Poisson process with a mean of 0.03 flaws per panel. 1- If one panel is randomly...

Homework Statement An independent, identically distributed sample, x = (x1, ... , xn) of size n, is drawn from a Poisson distribution, parameter A. We want to test the null hypothesis H0 : A = A1 against the alternative hypothesis H1 : A = A2 where A1 < A2. Write down the likelihood ratio...

Hello I just found this forum, was recommended it by a person that I know and have a small probability question regarding Poisson distribution. Let (T,U) be a to dimensional discrete stochastic vector with the probability function p_{T,U} given by. P(T=t, U = u) = \left{...

My question is a bout this question below (Bear with me people) A tie bar 25mm in diameter and 1m long extends in length by 1.2mm, when subjected to an axial tensile force of 80KN. If the diameter decreases by 0.007mm, determine the values of poisson's ration, and E,G and K. My question...

If you have the metric g_{ab} , \pi _{ab} as the metric and "generalized momenta", my question is if you can define GR using Poisson Bracet: \dot g_{ab} =[g_{ab},H] \dot \pi _{ab}=[\pi _{ab},H] and hence use these equations to obtain and solve the metric.:shy:

Ok, If the mean time between a single random event occurring is 6 months then is the most probably month for the third event to occur the 18th month? Thanks!

Hi, in a Poisson Distribution test, what happens when the amount of time is doubled? For example, in 1 month, lamda=np and I can calculate the probability of x events happening in that 1month. However, if the question is changed to 6 months, what will i have to do? Thanks.

I need to show using Poisson brackets that: \left( \frac{\partial}{\partial t} \right) {f,g} = \left( \frac{\partial f}{\partial t} , g} \right)+ \left( {f, \frac{\partial g}{\partial t} \right) I know that: (f,g) = \left( \frac{\partial f}{\partial q} \frac{\partial g}{\partial p}}...

Hi. I've been wondering about the following and haven't made much progress on it. (Note that I've also posted this in the relativity section since the ultimate aim of this is to apply it to canonical relativity but since this is essentially a question about tensors I thought I'd put a copy here...

Hi. I've been wondering about the following and haven't made much progress on it. To set the scene, consider the following. Suppose that we have some sort of discrete theory in which the phase space variables are q^i and p_i. If we have some functions F(q,p) and G(q,p) we can define their...

Hey, I want to write a Computer Simulation in C++, which simulates the development of a DNA sequence with a probability to mutate x in one "generation". I do have a variable number (=n) of copies of this DNA. Now one might think, to simulate the mutation by simply: sum(n*Poisson distributed...

Hi to everyone. I am a new member in this forum. I was wondering if there is a rigorous proof on to how one passes from Poisson brackets to commutor relations in QM. Any help on that would be appreciated.

If we have (Poisson sum formula) in the form: \sum_{n=-\infty}^{\infty}f(n)= \int_{-\infty}^{\infty}dx f(x) \omega (x) with \omega (x) = \sum_{n=-\infty}^{\infty}e^{2i \pi nx} Then my question is if we would have that: \sum_{n=-\infty}^{\infty} \frac{ f(n)}{ \omega (n)} =...

Consider a poisson process one (P1) with a frequency 'a' and if it happens 'k' times you get (e^-a)(a^k)/k! and then you have another posssion processs that happens in the same time frame of P1 called P2 with a frequency of 'b' and if it happens 'z' times you get (e^-b)(b^z)/z! So what is...

Suppose the probability is 0.8 that any give person will believe a tale about the transgression of a famous actress.what is the probability that (a)the sixth person to hear this tale is the fourth one to believe it? (b)the third person to hear this tale is the first one to believe it? can...

Hi do u know if the poisson distribution has always the same value for EX(mean value) and variance?

I just want to check my answers/reasoning as I'm not sure if I assumed the right things to do these problems. N = {N(t), t>=0} ~ Poisson(1) and N_{(t,t+h]} = N(t+h)-N(t) Determine P(N(4) =3|N(2) = 1) Here I presumed that since N(2) = 1, then there must be 2 more arrivals in the interval...

Okay, I'm a geek with a lot of time on my hands, so I'm going through all the problems in Sakuri. The problem: Calculate [x^2,p^2] . Simple enough. There are basically two fundamental attacks to do this. 1. Direct computation. I get that [x^2,p^2]=2i \hbar (xp+px) , which I got both by...

Hello I'm Presented with the following Poisson distribution question P(X = x) = \frac{e^{-\lambda} \cdot \lambda^{x}}{x!} where x \in (1,2,3,\ldots) and \lambda > 0 Then I'm suppose to show that the above can be re-written if P(X \leq 1) = 1 - e^{- \lambda} Any idears on how I...

Consider the following general Hamiltonian for the electromagnetic field: H = \int dx^3 \frac{1}{2} E_i E_i + \frac{1}{4}F_{ij}F_{ij} + E_i \partial_i A_0 + \lambda E_0 where \lambda is a free parameter and E_0 is the canonical momentum associated to A_0, which defines a constraint (E_0 =...

The problem is the following; N has a geometric distribution with Pr(N=0)>0. M has a Poisson distribution. You are given: E(N) = E(M); Var(N) = 2Var(M) Calculate Pr (M>1). From general knowledge we know that the expected value of a variable in a geometric distribution E(N) =...

Poisson Distrobution-HELP! URGENT! the problem: The Breakdowns of a robot follow a Poisson Dist. with an avg of .5 breakdowns per 8-hour workday. If this robot is placed in service at the beginning of the day, find the probability that: a. It will break down durring the day. b. It will...

Could anybody attempt to solve this probability question? It incorporates the Poisson Distribution. Thank You. A company finds that it issues a mean of 7 pairs of earplugs a week to any employee. What is the probability that the number of pairs taken by any employee is 9 per week? (Using the...

I'm having a bit of trouble in coming up with the solution for this question A hard disk manufacturing process desposites a thin coating of magnetic material on a plastic substrate. Empirical measurement has shown that the process introduces 20 defects per 15000cm squared. A disk pack...

Hi there, I'm a bit stuck and was hoping somebody could give me a couple of pointers... A lecturer wages that at least one pair of students in his class have birthdays on the same day. What is the minimum number of students in his class for him to be likely to win the bet? I have assumed...

I am attempting a past paper question from school, i don't have the answer (and it doesn't look like i will anytime soon!) The question: "The Random variable X has a poisson distribution with mean 4. The random variable Y is defined by Y = 4X + 1 Find the mean and standard deviation...

For a binomial distribution with n=10 and p=0.5 ,we should not use the poisson approximation because both of the conditions n>=100 and np<=10 are not satisfied. SUppose we go way out on a limb and use the Poisson aproximation anyway. Are the resulting probabilities unacceptable...

If I have an infinite slab of incompressible self-gravitating fluid of density rho within the region |z|<a, and I am asked to find the potential both inside and outside the slab, where should I start?

so flaws in metal produced by high temperatures occur at a rate of 1 per 10 square feet. what is the probability that there is 3 or more flaws in a 8 x 5 feet. ok, so I know we need to use poisson disstribution on this, e^-np * np^k/k!. howver, I don't know my np. so 1 per 10 square...