# Tagged Questions

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### How would I find the PDF of one poisson variable in terms of another?

I am looking for the PDF of a Poisson variable. The setup is that pit crews are working on racecars on the track after the drivers reports trouble. The pit crew's expected work time is exponentially ...
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### conditional mean of geometric RV

Say, there are three nodes: $S$, $R$, $D$. $S$ transmits to $R$, $R$ stores the packets, and later transmits to $D$. At any time, either $S$ or $R$ is selected to transmit according to some random ...
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### Probabilistic model of parallel web servers

Note: The following probabilistic model of parallel web servers is abstracted from an engineering project. I am not good at probability theory and I am seeking some evaluations and suggestions. ...
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### Question on M/M/s queue

costumers arrive to a service station according to a poisson prossees and on average 2 during an hour.the service times and independent of the arrivals and internally independent with mean 45 minuts ...
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### Proof of $\text{Poisson}(\lambda p)$-arrivals.

We have a queue where people pass out of it with $\text{Poisson}(\lambda)$ and they come in with probability $p$. I understand that the arrivals follow $\text{Poisson}(\lambda p)$, but how can ...
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### M/GI/1 service time distribution

I want to compute the distribution of the waiting time and the number of jobs for M/GI/1 where the service time is Heavy-Tailed or more specifically Pareto. I found this paper ...
Given a Poisson process (e.g. radioactive decay) with rate $\lambda$, then the expression $\exp(-\lambda t)$ is the probability of observing no counts in time interval $t$. This can be interpreted ...
Customers line up to be serviced according to a Poisson process at an average rate of five per hour. If the time it takes to serve one customer is a continuous uniform random variable on $[0,4]$, ...