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Questions tagged [poisson-distribution]

For questions relating to Poisson distributions in probability theory. To be used with [probability] or [probability-distributions] tag.

The PMF of a random variable $X$ distributed according to the Poisson distribution with parameter $\lambda > 0$ is the following: $$\Pr\left[X=k\right]=\frac{\lambda^k \exp(-\lambda)}{k!}\;,\; k\geq 0$$ This distribution describes the number of independent events occurring with constant rate in some unit time, the average being $\lambda$ events per unit.

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Chi-Squared Goodness of Fit Test for a Poisson Distribution

H0: It is a Poisson Distribution. H1: It isn't a Poisson Distribution. At the 5% significance level: degrees of freedom: k - 2 = 6 - 2 = 4 so a critical value of 9.49 Now I need to find: total number of burglaries/total number of weeks. In order to…
Oscar
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Obtaining the Poisson distribution in the calculator.

I want to calculate a Poisson that involves the calculation of $100!$ Does anyone know how to program it in a Casio calculator?
gibarian
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Necessary Assumptions when Deriving Poisson Distribution

Poisson distribution expresses the probability that a specific number of discrete independent events happen over a fixed time interval, as long as the events are sufficiently rare. To be precise, I accept the following premises for Poisson…
Samuel Hapak
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Numer of arrivals in merged Poisson Process, given number of arrivals in one process

I'm working on an exercise related to Poisson processes and have encountered a step in the solution that confuses me. The exercise is as follows: Consider two independent Poisson processes $X_1(t)$ and $X_2(t)$, where $X_i(t)$ represents the number…
Vlad Ionescu
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poisson distribution,and coding.

prove that if random variable, Y= k X, where k is a non-zero constant and X follows Poisson distribution with mean λ, then Y also follows Poisson distribution with mean kλ. Is it true, if then, How can I prove it?
anhoyong
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Poisson Race Problem

Let $X \sim Pois(\lambda)$ and $Y \sim Pois(\mu)$ be independent random variables that follow two different Poisson distributions, with $\lambda < \mu$, then we have $P(X-Y \geq 0) \leq e^{-(\sqrt\mu-\sqrt\lambda)^2}$, as demonstrated on the…
tdteach
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What is the poisson distribution?

So take this example. The number of ice creams sold per hour from Mr Fishy’s van is observed to be a Poisson random variable with parameter λ = 8. Each ice cream costs two pounds but Mr Fishy has to pay five pounds per hour for the pitch. What is…
Tingo Hugo
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Poison Distribution: Yearly event to monthly event

Consider the following question as example. When biking to school you have an average of 2 flat tires a year. What is the chance of having to flat tires in one month? I know how I'd use the Poisson Distribution to calculate the probability of zero…
O'Niel
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Nonhomogeneous Poisson distribution

Suppose claims arrive at a firm with nonhomogeneous Poisson distribution where: $\lambda(t)=$ {$t, \ 0\leq t\leq 5$ $5, \ 5\leq t\leq 7$ $12-t, \ 7\leq t \leq12$} (Sorry I don't know how to write the function out properly on latex) $t$ is the time…
Charlie P
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What does it mean to find $P(X=Y)$ for Poisson distributions?

So I have a mathproblem where the Poisson distribution of the number of flowers X in one area is given by $\lambda_1=4$. The Poisson distribution for the numbers of flowers Y in the other area is given by $\lambda_2=6$. I am then asked to find an…
Mathomat55
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$X\sim\operatorname{Pois}(2)$ and $Y\sim\operatorname{Pois}(5)$ are independent. How to obtain the mean and variance of $X-Y$?

If both random variables X and Y are Poisson then their mean is equal to their variance respectively. I thought of subtracting both means but I realise, how was I going to get the variance. Poisson distribution=(μ^x.e^-μ)÷(x!). Where μ= mean, X can…
Ernest
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Poisson probability gettting events over large periods

The problem reads like this: The number of calls the company receives is 4 per hour. a) Find probability to get exactly 5 between 09:00 and 12:00 of a given day b) Given that there the company has received at least 6 between 12:00-14:00, what is the…
Just_Newbie
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Setting mean value for Poisson subsampling

I'm running a machine learning algorithm in federated settings where participants collaboratively build a model by participating in the training rounds. At each training round, I need to sample a fixed number of participants, say 100 out of a total…
ABHS
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Probability across an interval using Poisson

Working through some Poisson probability questions and am wondering whether the knowledge of how many events have occurred changes a calculation. The question is thus: The number of prank calls received by an bartender is modeled using a Poisson…
Frank Anderson
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Can someone explain to me why the mass formula, the expected value formula, and the variance formula for Poisson distribution?

Can someone explain to me why the mass formula for Poisson is $P(X=x)=\cfrac{e^{-\lambda}\lambda^x}{x!}$? Also why the expected value is $E(X)=\lambda$ and Variance is $Var(X) = \lambda$? My book only gives the formula for mass and no explanation.…
user865043
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