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In a Poisson process with mean $\lambda$ the probability that n events occurred in [0,t] is...Given that an Poisson arrival has occurred in an interval [0,t], where t is geometric with mean (alpha).
Is it true that the arrival instant is uniform in [0,t]?
Let $T$ be the time of the first arrival, let $\tau$ be an arbitrary time between 0 and t, and let the Poisson distribution have a mean of $\lambda$ arrivals per unit of time.Given that an Poisson arrival has occurred in an interval [0,t], where t is geometric with mean (alpha).
Is it true that the arrival instant is uniform in [0,t]?
I apologize for the fact that at first I didn't realize that t is a geometric r.v. and not a deterministic r.v., so that I have to better specify my answer. In general in a stationary Poisson process with mean $\lambda$ the probability that n events occur in a time between $\tau$ and $\tau + t$ is...Given that an Poisson arrival has occurred in an interval [0,t], where t is geometric with mean (alpha).
Is it true that the arrival instant is uniform in [0,t]?