Probability/Poisson Problem

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Suppose that cars travelling at night on a freeway arrive at a toll station according to a Poisson process with rate alpha @=5 per minute. If five cars arrived in [0,3] (that is, during a three minute period starting at midnight), what is the conditional pmf of the number of cars that arrived in [0,1] (during the first minute of the period)?
 

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  • #2
Welcome to PF

What do you mean by pmf? Probability mass function?

Anyways, You condition on the even that up t=3 five cars arrived. what do you know about the conditional distribution of the arrival times of these five cars?

Hint: It's a famous property of the Poisson process because of which it is sometimes referred to as the "most random" point process of all.
 

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