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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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Why are non-homogenous poisson processes not independent?

Why are non-homogenous poisson processes not independent? Let $ N (t)$ be a non-homogeneous Poisson process with intensity $\lambda t$, t > 0. Find the joint density of the first two sojourn times, and deduce that they are not in general…
jj238sdfaaa
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Poisson process/probability

Calls are distributed according to Poisson process at an average rate of 12 calls per hour. Calls are usually handled at the basic sales level, but if there is a more complicated case, the manager will need to be involved. The probability that an…
user218698
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in a poisson-distribution, why is the probability of e-1 the same as e?

I'm not sure if I'm doing it wrong, but I checked the Wiki page, and there seems to be 2 maximum points regardless of input, which the probability of getting the expected value minus 1 the same as getting the expected value. Why is this?
user163693
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cookie problem ; solution by Poisson approach doesn't matches binomial one

here's the problem. A company produces chocolate chip cookies. number of piece of choco chip per one cookie is 2.5 (in Poisson average). These cookies are boxed with 20 pieces together. what's the possibility, that every 20 cookies contain at least…
서영빈
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Poisson distribution car profit

A firm has $10$ cars for hire, the hire charge for each of which is $250$ dollars per day. The overheads are $25$ dollars per car per day, whether or not they hired. If the daily demand for cars has a Poisson distribution with mean $8$, what is the…
Chloe
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Poisson-distribution, expactancy value E[X²]

I want to solve this: $E[X^2]=\sum_{k=0}^{\infty} k^2 e^{-\lambda}\frac{\lambda^k}{k!}$ My try: $E[X^2]=\sum_{k=0}^{\infty} k^2 e^{-\lambda}\frac{\lambda^k}{k!}=\sum_{k=1}^{\infty} k^2 e^{-\lambda}\frac{\lambda^k}{k!}$ Indexshift and…
ChamDao
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Poisson Distribution homework

I need some help in the next example, as it could be in the exam next week. Description: We are collecting seashells at the beach, and we find that out of 300 seashells 4 are nautilus. What's the probability that from the next 100 seashells we pick…
Andrew
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Poisson Processes and Insurance

An insurance company receives a certain number of claims of week that are Poisson distributed at a $\text{rate} = 10$. The amount of each claim is exponentially distributed with $\text{mean} = \$1,\!000$. Calculate: a) The mean and variance of the…
StatVoyager
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Poison distribution question Stats

A busy railway station has two taxi stands at separate exits, A and B. At stand A, taxis arrive according to a Poisson Process of rate 2 per minute. Assume that any arriving train passenger who requires a taxi goes to stand A with probability 0.7 or…
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