Poisson Definition and 509 Threads

In order to understand how related are the theories of General Relativity and Electromagnetism, I am looking at the electric and magnetic parts of the Weyl tensor (in the ADM formalism) and compare them with the ones from Maxwell's theory. I have tried to look at the Poisson bracket, but the...

Hello all. I am working on a problem and I am getting a bit confused. Suppose we have a poisson equation that we wish to solve subject to certain boundary conditions. Let's say we are in 1D (we can later extrapolate to more dimensions). Is it possible to impose Dirichlet boundary...

Hi, Suppose we look at two dimensional Poisson's equation in a medium with spatially varying (but real) dielectric constant: \nabla(\epsilon_r\nabla \varphi) = -\frac{\rho(x,y)}{\epsilon_0} Consider the problem of solving this using the Finite Difference method on a rectangular grid...

Hi! I do have this problem - Consider that for a set of values, I do have a Poisson distribution with mean value <m> - Now, I need to gather another set of dataset, which I should vary the mean value by 5% - My question is, how can I translate each one of these new values to sigma deviations...

Homework Statement Considering the Hamiltonian for a harmonic oscillator: H=\frac{p^2}{2m}+\frac{mw^2}{2}q^2 We have seen that the equations of motion are significantly simplified using the canonical transformation defined by F_1(q,Q)=\frac{m}{2}wq^2cot(Q) Show explicitly that between both...

Given that an Poisson arrival has occurred in an interval [0,t], where t is geometric with mean (alpha). Is it true that the arrival instant is uniform in [0,t]?

Homework Statement During a two hour window, people are given the option of calling number X, donating $9.90, or number Y, donating $0.50. X is Poisson distributed with 1500 calls/minute. Y is Poisson with 3750 calls/minute. What is the probability that more than $2,000,000 is raised...

So I have a histogram with bins that contain the number of events expected at a specific energy (which I generated with a Monte Carlo).. I need to add (integrate) all the bins in a section of this histogram and find the error of this value. However, the number of events are very small approx...

Hi, Homework Statement I am somewhat perplexed by the proposed solution to the following Statistics problem and was hoping one of you might be willing to help me settle this: An operator receives phone calls between 8AM and 4PM at an average rate of 20 calls/hour. No call was received during...

l know you can define poisson brackets between two analytic function in several variables f(q1,q2,q3,..,p1,p2,p3,..) and g (q1,q2,q3,..,p1,p2,p3,..) only by foundamental poisson brackets and their proprieties.how is it possible?

Homework Statement Prove the Poisson summation formula. Homework Equations The Attempt at a Solution Correction to image below: the very last line of the theorem (italicized) should say f hat is the Fourier transform, not f(n). Does this proof make sense and is it...

Homework Statement X_t and Y_t are poisson processes with rates a and b n = 1,2,3...Find the CDF F_X{}_t{}_|{}_X{}_t{}_+{}_Y{}_t{}_={}_n(x)Homework Equations The Attempt at a Solution F_X{}_t{}_|{}_X{}_t{}_+{}_Y{}_t{}_={}_n(x) =P(X_t<x|X_t+Y_t=n) =\frac{P(X_t<x,X_t+Y_t=n)}{P(X_t+Y_t=n)} Not...

Radioactive Decay Probability? Say you are counting the number of decays and the time of observation is varied. I know that as time increases, the Gaussian Distribution becomes a closer fit to the observed probability than when the time interval takes smaller values because the mean count...

Hello, for the Poisson problem Δu = -1 on a 2D circular disk with u = 0 on the boundary, we have average(u) = \frac{1}{8\pi}Area(disk), which is easy to see, as the solution is quadratic in the polar coordinate r. Does this (or a similar) relation hold for non-circular 2D domains? This...

Homework Statement Show that the Poisson probabilities p_{0}p_{1},... can be estimated recursively by p_{0} = e^{-\lambda} and p_{k}=(\lambda/k)*p_{k-1} k=1,2,... Homework Equations I know the Poisson distribution f(x, \lambda) = e^{-\lambda}\lambda^{x}/x! But I...

Homework Statement Consider a one-way road where the cars form a PP(lambda) with rate lambda cars/sec. The road is x feet wide. A pedestrian, who walks at a speed of u feet/sec, will cross the road if and only if she is certain that no cars will cross the pedestrian crossing while she is on...

Homework Statement A trial consists of throwing 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...

Hello PF This might be a fairly simple question to most of you, but I was given this problem (don't worry, I already solved it just wondering about something) Suppose the probability of suffering a side effect of a certain flu vaccine is 0.005. If 1000 persons are inoculate, find the...

Hello! I was reading a journal article on modeling the interaction between different neural networks and I am confused about the follwoing method (cited below). It is describing the spike rate output of a neuron based on oscillating firing rates of excitatory (E) and inhibitory (I) inputs...

Homework Statement I was given two problems and required to calculate some statistics/parameters for them. They are: 1) The Vancouver Island Marmot is one of Canada’s most endangered species; there are currently only 63 animals left on the Island. To maintain the population, geneticists...

Homework Statement If the number of complaints a dry cleaning establishment receives per day is random variable having the Poisson distribution with λ = 3.3, what are the probabilities that it will receive: (a) Five complaints altogether on any two given days. (b) at least 12 complaints...

1. A Poisson random variable is such that it assumes the values 0 and 1 with equal probability. Find the value of the Poisson parameter, ρ ,for this variable. 2. Poisson equation: f(x) = e-λs(λs)/x! 3. I assumed the probability would be 0.5 because it can be either 0 or 1. 0.5 = e-λs(λs)/x! But...

Hi, Suppose you have a collection of fields \phi^i (t,x) depending on time and on 1 space variable, for i=1,...,N. Its dynamics is defined by the Lagrangian L=\frac{1}{2} g_{ij}(\phi) (\dot{\phi}^i \dot{\phi}^j - \phi ' ^i \phi ' ^j ) + b_{ij}(\phi) \dot{\phi}^i \phi ' ^j where...

Since I couldn't find any reference on the subject of Poisson bracket formalism of classical field theory, I'm posting a few question here: A) What are the Poisson brackets of the source-less EM field? B) Does the law that the Poisson brackets between a dynamical variable and its conjugate...

I want to find [M_i, M_j] Poisson brackets. $$[M_i, M_j]=\sum_l (\frac{\partial M_i}{\partial q_l}\frac{\partial M_j}{\partial p_l}-\frac{\partial M_i}{\partial p_l}\frac{\partial M_j}{\partial q_l})$$ I know that: $$M_i=\epsilon _{ijk} q_j p_k$$ $$M_j=\epsilon _{jnm} q_n p_m$$ and so...

Hi, Referring to Jackson's Electrodynamics 3ed, page 197, line 5. He assumes that the magnetization can be divided into volume part and surface part, thus generating eqn 5.100. This is fine. In a straightforward way, I wanted to do the same but for electrostatics, eqn 4.32:∅= (1/4πε) ∫dv...

Homework Statement Solve the equation: ∂2F/∂x2 + ∂2F/∂y2 = f(x,y) Boundary Conditions: F=Fo for x=0 F=0 for x=a ∂F/∂y=0 for y=0 and y=b Homework Equations How can I find Eigengunctions of F(x,y) for expansion along Y in terms of X? The Attempt at a Solution I can't imagine...

Homework Statement Consider ##n## independent trials, each of which results in one of the outcomes ##1,...k## with respective probabilities ##p_1,...p_k, \sum_{i=1}^{k} p_i = 1##. (I interpret this summation as just saying mathematically that definitely one of the outcomes has to occur on each...

Why Poisson kernel is significant in mathematics? Poisson kernel is ##P_r(\theta)=\frac{1-r^2}{1-2rcos\theta+r^2}##. http://www.math.umn.edu/~olver/pd_/gf.pdf page 218, picture 6.15. If we have some function for example ##e^x,sinx,cosx## what we get if we multiply that function with Poisson...

Dear all I am working with a Gamma-Poisson mixture distribution where (and this is not usual) the support of the Gamma distribution (in fact, I am able to restrict to the neg exponential instead of the Gamma...) is finite, e.g. [0,1]. I would like to derive the mean and a Likelihood...

Homework Statement Let X_1,...,X_n be a random sample from a poisson distribution with mean \lambda Find the MLE of \lambda^2 + 1 Homework Equations The Attempt at a Solution I found \hat{\lambda}=\bar{x} Can I just square it and add 1 and solve for lambda hat? If not I have no idea...

Hello, hopefully this is the right place. This is a homework question, so it should definitely be in this forum, but I wasn't sure which sub-forum to put this rather elementary stats question. Homework Statement In my introductory mathematical statistics class, we've been given the...

Homework Statement Suppose x has a Poisson \lambda distribution Find the probability generating function and range it is well defined. Then evaluate E[x(x-1)(x-2)(x-3)(x-4)(x-5)(x-6)(x-7)(x-7)(X-8)(x-9)(x-10)(x-11)] Homework Equations f_x (x) = exp(-lamda) (lamda)^x/x! for...

Let Y|X be a Poisson(X), and X be Gamma(\alpha, \beta). Find E(X|Y)... Since Y|X is Poisson(X), we have f(Y|X)= \frac{m^x e^{-m}}{x!}... Since X is Gamma(\alpha, \beta), we have f(x)= \frac{x^{\alpha-1} e^{-x/B}}{\Gamma(\alpha) \beta^{\alpha}}... Since f(Y|X) = \frac{f(x,y)}{f(x)} ====>...

Okay there is a particular equation in my book, which I just can't seem to understand intuitively. I've been staring at it for an hour now without progress, so I hope some of you can explain it. Basically it's the one on the attached picture. Let me introduce the notation so you can help me...

Homework Statement Homework Equations The Attempt at a Solution Here's what I've tried so far, not really sure how to go on with these problems. Been reading the textbook up and down on Poisson processes! Any hints or help? Especially 1.B, 1.C and 2.B, 2.C

Hello, I want to be able to model something with a poisson process with an intensity function that changes with both time and space. Let's say for example that the time interval I'm considering is 100 hours long and I believe that the intensity function increases at a constant rate so that...

What is the significance of the Poisson kernel (besides solving the Dirichlet problem)? What is the Poisson's role in solving the Dirichlet problem? I know it is the solution but what is meant by its role?

Prove: $$ \lim_{r\to 1}P(r,\theta) = \begin{cases} \infty, & \theta = 0\\ 0, & \text{otherwise} \end{cases} $$ For the first piece, take the summation $$ P(1,0) = \frac{1}{\pi}\left(\frac{1}{2} + \sum_{n = 1}^{\infty} 1^n\right). $$ Then $\sum\limits_{n = 1}^{\infty} 1^n = \infty$. Therefore, we...

For a fixed $r$ with $0\leq r < 1$, prove that $P(r,\theta)$ is an even function.Take $-r$. Then \begin{alignat*}{3} P(-r,\theta) & = & \frac{1}{2\pi}\frac{1 - (-r)^2}{1 - 2(-r)\cos\theta + (-r)^2}\\ & = & \frac{1}{2\pi}\frac{1 - r^2}{1 + 2r\cos\theta + r^2} \end{alignat*} I have $1 +...

Homework Statement Consider the Klein-Gordan action. Show that the Noether charges of the Poincare Group generate the Poincare Algebra in the Poisson brackets. There will be 10 generators.Homework Equations \{ A,B \}=\frac{\delta A}{\delta \phi}\frac{\delta B}{\delta \pi}-\frac{\delta...

Hi! I'n my quantum mechanics homework I've been asked to proved the Poisson summation formula. The mathematicians seem to use abstract and confusing notation when proving this kind of thing so I'm hoping for some help from physicists in standard notation ;) I'm starting with a function f(x) =...

I cannot seem to get the first moment of Poisson's distribution with parameter a: P(n_1)=\frac{a^{n_1}e^{-a}}{n_1!} when using the characteristic function \phi _X (k)=\exp [a(e^{ik}-1)]. The definition of the first moment involving the characteristic function is <n_1>=\frac{i}{n} \frac{d \phi...

In general, if A~Po(a) and B~Po(b) are independent random variables, then C = (A+B)~Po(a+b). Can someone please explain the intuition/simple proof of this and a word problem or example would really help to reinforce this concept. Thanks.

Homework Statement Let f(q, p), g(q, p) and h(q, p) be three functions in phase space. Let Lk = εlmkqlpm be the kth component of the angular momentum. (i) Define the Poisson bracket [f, g]. (ii) Show [fg, h] = f[g, h] + [f, h]g. (iii) Find [qj , Lk], expressing your answer in terms of...

Hey guys, In class, I was shown that the Binomial prob density function converges to the Poisson prob density function. But why does this show that the Binomial distribution converges in distribution to the Poisson dist. ? Convergence in distribution requires that the cumulative density...

Hi friends I am trying to drive constraints of a Lagrangian density by Dirac Hamiltonian method. But I encountered a problem with calculating one type of Poisson Bracket: {\varphi,\partial_x\pi}=? where \pi is conjugate momentum of \varphi. I do not know for this type Poisson Bracket I can...

Hello everybody! I am using in my studies this beautiful book by Kippenhahn & Weigert, "Stellar Structure and Evolution", but I have some problems about collapsing polytropes (chapter 19.11)... After defining dimensionless lenght-scale z by: r=a(t)z and a velocity potential \psi...

Suppose a person takes data (say counts per minute of cars going past his window), for a long time. Then he loses his data, but knows that he counted 5 cars more often than any other number. What is the likely range for the average count rate? I tried to solve this by saying the mode is 5, so...

1. The number of times that a person contracts a cold in a year is a Poisson random variable with parameter lambda=5. Suppose a wonder drug reduces the Poisson parameter to lambda=3 for 75% of the population but does not affect the rest of the population. If an individual tries the drug for a...