Question: At times that form a Poisson process at rate = 25 (per hour), people rent a Citibike, and independently they use it for a random

At times that form a Poisson process at rate = 25 (per hour), people rent a Citibike, and independently they use it for a random amount of time distributed as continuous Uniform(0,8) (hours) then return it. Assume initially, at

time t= 0, there were no Citibikes rented out, and also assume that there are an unlimited number of Citibikes

Suppose that instead of each person having the same rental distribution time,

each person, independently with probability p= 0 .2 has a Uniform (0,8) distribution while with probability 0.8 has an exponential distribution at rate 1/4. What is the probability that at time t= 1 there are 20 Citibikes rented out with the exponential rental times given that there are 30 rented out at time t= 1 with the Uniform (0,8) distribution?

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