Poisson distribution Definition and 127 Threads

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 $$F(x)$$.

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 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...

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∞...

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 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...

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...

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...

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...

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.

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...

I have been analyzing some data at work, and I have measured the occurrence rates of some event. How do I give a one sigma confidence interval to go along with it, assuming it is a Poisson event? For example, I found that something occurs 20 out of 10 000 times, something else occurs 43 out of...

Hi, I have a problem with determining the probability distribution function of the number n of detector counts in a given time t. I am assuming the events follow exponential distribution ε(t,λ) = λexp(-λt). Now if that was everything it would simply be a Poisson distribution, however, what I...

The number of cracks in a section of interstate highway that are significant enough to require repair is assumed to follow a Poisson distribution with a mean of two cracks per mile. What is the probability that there are no cracks that require repair in 5 miles of highway? any help guys? :)

A building has 2 independent automatc telephone exchanges A and B. The number X of wrong connections for A in anyone day is a poisson variable with parameter 0.5 and the number Y of wrong connections for B in any one day is a poisson variable with parameter 1. Calculate in any particular...

Homework Statement X(t) is a Poisson process with \lambda=0.2 events per second. What is the probability of zero events in 45 seconds? 2. The attempt at a solution \frac{45}{0.2}=225 (0.2 second intervals) so P[X=0] in 225 consecutive intervals is: \left(e^{-0.2}\right)^{225} = 2.86...

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'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 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'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...

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...

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...

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 On average, 2.5 telephone calls per minute are received at a corporation's switchboard. Making appropriate assumptions about the distribution ( provide justification ), find the probability that at any given minute there will be more than 2 calls. Homework Equations No...

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...

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...

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...

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 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...

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}...

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...

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...

probability of event occurring -- poisson distribution? I am the keeper of records for my local Volunteer Fire Dept. I have now collected data for each of our incident calls from the last 3 years and have made some _very_ basic stabs at interesting statistics which you can see at...

Hey guys, I'm kind of stuck on this question. In a certain town, crimes occur at a Poisson rate of 2.4 per month (i.e. according to a Poisson process with a rate of 2.4 per month). What is the probability of having exactly 2 months (not necessarily consecutive) with exactly 4 crimes during...

Homework Statement X is a discrete random variable that has a Poisson Distribution with parameter L. Hence, the discrete mass function is f(x) = L^{x} e^{-L} / x!. Where L is a real constant, e is the exponential symbol and x! is x factorial. Without using generating functions, what is...

Homework Statement On average, each of the 18 hens in my henhouse lays 1 egg every 30 days. If I check the hens once per day and remove any eggs that have been laid, what is the average number, μ, of eggs that I find on my daily visits? What is the most probable (whole) number of eggs that I...

Nr of customers arriving at a shop follow Poisson. In 15, an average of 4 customers arrive. a) A customer has just arrived. Then a minute passed and no one arrived. What is the probability of it takoing at least 5 more min. until another customer arrives? b) Consider 40 non-overlapping...

Homework Statement 1. Suppose that the number of telephone calls an operator receives from 9:00 to 9:05 A.M. follows a Poisson distribution with mean 3. Find the probability that the operator will receive: a. no calls in that interval tomorrow. b. three or more calls in that interval the...

Homework Statement LEt X have a Poisson distribution with u=100. Use Chebyshev's inequality to determine a lower bound for P(75<x<125) Homework Equations Chebyshev's Inequality. The Attempt at a Solution I'm really unsure of how to go about calculating this problem. Any help...