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How can I prove that $X+Y$ is a Poisson process with parameter $\lambda_X+\lambda_Y$?

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#markov-process #poisson-process #poisson-summation-formula
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A Poisson-like process with intensity controlled by a Markov chain

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Proving that a process is a Poisson Point Process

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#probability-theory #stochastic-processes #poisson-process #point-processes
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Time dependent Poisson arrival rate in wait-time theory

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#mathematical-modeling #poisson-distribution #poisson-process
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Exercise on composition of Poisson processes

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#probability #poisson-process
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Exercise about the Poisson approximation

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Let $\{X(t); t\ge 0\}$ be a Poisson process with rate $\lambda =2$. Find the probability $\Pr\{X(1)\le 2\}$.

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Calculating the mean in a Poisson process

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194
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Plausible to assume that a certain random variable has a Poisson distribution

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Number of events of Poisson process A until first occurrence of Poisson process B

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Salvaging particular solution of arrival at the train station problem

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#probability-theory #poisson-process
58
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Probability theory of Vapnik

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Exponential distribution (probability of exact number)

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About the value of $\mathbb{P}(N(t)=10,N(t/2)=5|N(t/4)=3)$ where $(N(t))$ is a Poisson process

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Poisson and exponential distribution for independent rvs

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