Question

Hello! I am having trouble with a question from my stochastic processes class. Any help would be much appreciated!

Traffic on Snyder Hill Road in Ithaca, NY, follows a Poisson process with rate 2/3’s of a vehicle per minute. 10% of the vehicles are trucks, the other 90% are cars.
(a) What is the probability at least one truck passes in a hour?
(b) Given that ten trucks have passed by in an hour, what is the expected number of vehicles
that have passed by.
(c) Given that 50 vehicles have passed by in a hour, what is the probability there were exactly 5 trucks and 45 cars.

Answer 1

G) Given that 5o vehicles have posed by in hou The average numberof vehicles passedbyin an hour λ290 The probability that o vehicles passed is s01 The probability that exactly s huc is 5-4 21! SI The probabilty thot exact y 4s cars is 732 e-A2-364を360.09, 4S/ Given that 50 vehictes have possed bt in an hour the probabilty -there were exactly 5 trucks and 45 cars is

p(x 50) Sine, the mumber of trucks and cars are indeperdent pCxrS/x; 45) = 0.003276 ,'、Geuen that So uehicles have passed by in an hour , the pickability there werc cxactly 5 trucks and 4S cars is 0.185