Suppose that the number of vehicles passing by the stadium entrance A can be modelled by a homogeneous Poisson process with the rate of 10 vehicles per minute, 15% thereof being lorries and 85% being cars. Suppose that the types of particular vehicles are independent. (a) Find the probability that in 3 mins, at least one lorry passes the stadium entrance A. (b) Suppose that during the first minute of observation, exactly 12 lorries have passed by. Find the expected number of the cars passing the entrance during the same period. (c) Suppose that during the first minute of observation, exactly 15 vehicles have passed by. Find the probability that among these vehicles, there were exactly 3 lorries and 12 cars. (d) What is the probability that the first four arriving vehicles are all cars?
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What do you know about a splitting Poisson process? Do you have any thoughts on this problem? – Matthew H. Apr 18 '21 at 16:48
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If you show some attempts I'd enjoy guiding you to the solution. – Matthew H. Apr 18 '21 at 23:13