The number of calls per hour arriving at an answering service follows a Poisson process with lambda = 4.
It is known that exactly "k" calls arrived in the first four hours. What is the probability that exactly j of them arrived in the first hour?
I think I'm stumped on the setup. I know its a conditional probability but the events aren't independent, correct? Also, I know how to add Poisson rvs, and that x4 can be changed to be a poisson with lambda = 16.
P(x1 = j | x4 = k) ?
It is known that exactly "k" calls arrived in the first four hours. What is the probability that exactly j of them arrived in the first hour?
I think I'm stumped on the setup. I know its a conditional probability but the events aren't independent, correct? Also, I know how to add Poisson rvs, and that x4 can be changed to be a poisson with lambda = 16.
P(x1 = j | x4 = k) ?