# Questions tagged [poisson-distribution]

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

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### Question on Poisson Process

I am trying to solve the following problem: Jhon is a newspaper vendor. His customers arrive according to a Poisson process with a rate of one per minute. At any given moment, what is the probability ...
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### generalized poisson moment function approach to initalize input output model

I am trying to understand how the Generalized Poisson Moment Functions apporach is a way to initalize the nominator and denominaor of a LTI-Model that describes the connection between Input and Output ...
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### How can I calculate the rate of overlapping events between two Poisson processes?

I have the following problem: I have 2 independent Poisson processes with a known rates λ1 and λ2. The events in each process have a well-defined duration, D1 and D2. From that, I need to know: What ...
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### Poisson Question - number of signals received at station A

the question: ...
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### Probability of two independent random variables are equal decreases when they are more spread out

Let $X_{1},X_2\sim Bin(n,p)$ be iid binomial random variables. Then it is intuitive that $\mathbb P(X_1=X_2)$ decreases when $n$ increases (keeping $n$ fixes). However, it is not obvious to prove this ...
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### Expectation of a Poisson random variable

Let $N_{\lambda}$ be a random variable having Poisson distribution with probability mass function given by $$P( N_{\lambda} = k) = \frac { \lambda^k e^{- \lambda} }{ k!},$$ where $\lambda >0.$ ...
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### Why are the Binomial and Poisson probabilities different for frequency of a successful dice roll?

Why do I get different results using a Binomial vs Poisson process for calculating the frequency of a successful roll of a 6 sided die? Should I get the same answer calculating the same scenario with ...
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