A pedestrian wishes to go across a single-lane road where the cars arrive according to a Poisson process with the rate λ. The time needed for him to cross the road safely is denoted as k. He will have to wait until he sees a gap of at least k between the coming cars. If […]

A pedestrian wishes to cross a single lane of fast-moving tra c. Suppose the number of vehicles that have passed by time t is a Poisson process of rate , and suppose it takes time a to walk across the lane. Assuming that the pedestrian can foresee correctly the times at which vehicles will pass […]

I am really struggling with the Poisson Process. I am hoping someone out there can give me few hints or point me in the right direction with the following exercise. Let $\{X(t)\}$ be a Poisson process with arrival rate $\lambda>0$. Consider a “bridge” for this Poisson process. It is known that a Poisson process, $\{X(t)\}$, […]

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