Poisson Definition and 441 Threads

Homework Statement A rectangular field is gridded into squares of side 1m. at one time of the year the number of snails in the field can be modeled by a Poisson distribution with mean 2.25 per m^2. (i) a random sample of 120 squares is observed and the number of snails in each square...

Hi, I know the weak form of the Poisson problem \nabla^2 \phi = -f looks like \int \nabla \phi \cdot \nabla v = \int f v for all suitable v. Is there a similarly well-known form for the slightly more complicated poisson problem? \nabla (\psi \nabla \phi ) = -f I am writing some finite...

In Hamiltonian formulation there is an expression df / dt = { f , H } + ∂f / ∂t where f is function of q, p and t. While expressing Hamiltons equations of motion in terms of Poisson Bracket, i.e if the function f = q of p then its partial time derivative ∂f / ∂t becomes zero.. Please explain why?

Hello, I have this one problem but have no idea how to get started. Avg. number of accidents is .4 accidents / day (Poisson Process) What is the probability that the time from now to the next accident will be more than 3 days? What is the probability that the the time from now to...

If $$p(x=1)=p(x=2)$$ where $$x$$ follows a Poisson distribution, then find $$p(x=0 ~~or~~ 1) $$. Also find $$F(x)$$In connection with the above question, I have confusion about the last part i.e., about $$F(x)$$. I can find $$E(x)$$ here, but how to find $$F(x)$$.

Hi, I have a question about the definition of the poisson process. Check out the definition here: Would you say that one can prove point (2) from point (3)? The reason I have some discomfort about this is that something seems to be hidden in the poisson distribution to make it all work? For...

Homework Statement There are two stores A and B. Customers can equally enter one of the two stores, i.e., for a specific customer, the probabilities she enters store A or B both are 0.5. If the total number of customers in two stores has the Poisson distribution of parameter λ, then...

I've been asked to fit the histogram with a Poisson distribution as part of a mostly independent learning thing. The data was produced through a stochastic simulation. Can someone get me started on how I would go about finding the expected distribution? If you need additional information...

Homework Statement I made this question for myself to try to see if I could use two approaches (Poisson Distribution and Binomial Distribution) to solve a problem: Someone's average is to make 1 out of every 3 basketball shots. What are the chances she makes exactly 2 shots in a trial of 3...

I need some help on the following question: Let N() be a poisson process with parameter \lambda . I need to find that probability that N((1,2]) = 3 given N((1,3]) > 3 I know that this is equal to the probability that P(A \cap B) / P(B) where A = N((1,2]) and B = N((1,3]) >...

Okay, I'm trying to play around again :D A little overview; I know that the Poisson equation is supposed to be: uxx + uyy = f(x,y) I can manage to discretise the partial derivative terms by Taylor. I don't know how to deal with the f(x,y) though. Say for example, uxx + uyy = -exp(x). what...

Homework Statement Solve the equation \nabla^2\phi-\frac{1}{\lambda^2_D}\phi=-\frac{q_T}{\epsilon_0}\delta(r) substituting the \delta representation \delta(r)=\frac{1}{4\pi}\frac{q_T}{r} and writing the laplacian in spherical coordinates. Use as your guess...

## \int^{\infty}_{-\infty}dxe^{-ax^2}=\sqrt{\frac{\pi}{a}}## Is it correct also when ##a## is complex?

I have two questions: [SIZE="5"](1)As the tittle, if u(a,\theta,t)=0, is \frac{\partial{u}}{\partial {t}}=\frac{\partial^2{u}}{\partial {r}^2}+\frac{1}{r}\frac{\partial{u}}{\partial {r}}+\frac{1}{r^2}\frac{\partial^2{u}}{\partial {\theta}^2} and \frac{\partial^2{u}}{\partial...

When (canonically) quantizing a classical system we promote the Poisson brackets to (anti-)commutators. Now I was wondering how much of Poisson bracket structure is preserved. For example for a classical (continuous) system we have $$ \lbrace \phi(z), f(\Pi(y)) \rbrace = \frac{\delta...

Proving Some Poisson Bracket identities -- a notational question I need some help just understanding notation, and while this might count as elementary it has to do with Hamiltonians and Lagrangians, so I posted this here. Homework Statement Prove the following properties of Poisson's...

Homework Statement Show that Q_{1}=\frac{1}{\sqrt{2}}(q_{1}+\frac{p_{2}}{mω}) Q_{2}=\frac{1}{\sqrt{2}}(q_{1}-\frac{p_{2}}{mω}) P_{1}=\frac{1}{\sqrt{2}}(p_{1}-mωq_{2}) P_{2}=\frac{1}{\sqrt{2}}(p_{1}+mωq_{2}) (where mω is a constant) is a canonical transformation by Poisson bracket test. This...

Homework Statement Suppose that 1% of cars have defective brake lights and n cars are to be inspected. How large should n be for the sample to have a probability of at least 50% of containing a car with a defective brake light? Give an answer using a Poisson approximation with an appropriate...

Homework Statement Let X(t) and Y(t) be independent Poisson processes, both with rates. Define Z(t)=X(t)+Y(t). Find E[X(1)|Z(2)=2]. 2. The attempt at a solution...

Helmholtz equation:##\nabla^2 u=-ku## is the same form of ##\nabla^2 u=f##. So is helmholtz equation a form of Poisson Equation?

Hi there, Having done a Google, I wasn't able to find much information relating specifically to Poisson statistics and photon detections. I was wondering why photon detection experiments are calculated using Poisson statistics? (So for example, would Poisson distribution calculations be...

Homework Statement During the day, cars pass along a point on a remote road at an average rate of one per 20 minutes. Calculate the probability that; (i) in the course of an hour no car passes; (ii) in the course of 30 minutes exactly 4 cars pass;Homework Equations P(X = x) =...

Homework Statement Data from www.centralhudsonlab.com determined the mean number of insect fragments in 225-gram chocolate bars was 14.4, but three brands had insect contamination more than twice the average. Assume the number of fragments (contaminants) follows a Poisson distribution...

Can anyone derive the p.m.f. of Poisson distribution without mentioning the binomial distribution? The binomial deriving method put lambda = np and finally the binomial p.m.f. become the Poisson one as n goes to infinity. It seems that this is only proving that binomial distribution will...

Homework Statement t(s) = 1 15 30 45 60 75 90 105 120 135 N(counts) = 106 80 98 75 74 73 49 38 37 22 Consider a decaying radioactive source whose activity is measured at intervals of 15 seconds. the total counts during each period are given. What is...

Homework Statement Use the Poisson distribution W=(λ^n/n!)*e^-λ to calculate <n> Homework Equations <n>=ƩW*n The Attempt at a Solution Since W = (λ^n/n!)*e^-λ I wind up with <n>=[(λ^n/n!)*e^-λ]*n But I really don't know where to go from here. Should I do a Taylor Series. I've...

Homework Statement A random variable has a Poisson distribution with parameter λ = 2. Compute the following probabilities, giving an exact answer and a decimal approximation. P(X ≥ 4) Homework Equations P(X = k) = λke-λ/k! The Attempt at a Solution P(X ≥ 4) = Ʃk = 4∞...

Arrivals are Poisson distributed with parameter $$ \lambda$$. Consider a system, where at the time of arrival of a tagged packet, it sees $$N_Q$$ packets. Given that the tagged packet arrives at an instant $$t$$, which is uniform in [0, T], what is the probability that all $$N_Q$$ packets...

Homework Statement On the average, a grocer sells 4 of a certain article per week. How many of these should he have in stock so that the chance of his running of stock within a week will be less than 0.01? Assume Poisson distribution. Homework Equations The Attempt at a...

Homework Statement Column supports a mass on its' top. So force is downwards. Column properties: Do = 50mm (outer dia) Di = 40mm (inner dia) E = 250 GNm^-2 (modulus of elasticity) V = 0.33 (Poissons ratio) Homework Equations Poissons ratio = Transverse strain = - εt / εl Transverse strain...

Homework Statement In a lengthy manuscript, it is discovered that only 14% of the pages contain no typing errors. If we assume that the number of errors per page is a random variable with a Poisson distribution, find the percentage of pages that have: Exactly one typing error, At the most 2...

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...

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...

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 [SIZE="5"]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...

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...