A bus arrives at a bus stop according to a Poisson process with lambda = 2 per hour. Assume that the amount of time, the bus spends at the bus stop is negligibly small. a. What is the probability that no busses will arrive in the first 45 minutes? b. What is the probability that the first bus will take more than 45 minutes to arrive? c. What is the probability that no busses arrived from 17:00 to 17:30, but 2 busses arrived between 17:40 and 18:10? d. A passenger just missed the bus, what is the probability that it will take more than 30 minutes for the next bus to arrive? e. Two types of busses service this stop (regular bus and articulating). The probability of the arriving bus being articulating is 1/4. Describe the time until the arrival of the second articulated bus using am appropriate probability function ? f. What is the PMF for F, the number of articulating bus arrivals between two consecutive regular bus arrivals? g. A tourist arrives at the bus stop and wishes to observe both of the bus types. What is the expected amount of time the tourist will spend at the bus stop to observe both types of busses? h. An individual arrives at the bus stop and waits for the bus. Due to their impatience, they call a ride-share for a ride from the bus stop. The driver will arrive at a time described by an exponentially distributed random variable with expectation of 15 minutes. What is the probability that the bus arrived first?
A bus arrives at a bus stop according to a Poisson process with lambda = 2 per hour. Assume that
the amount of time, the bus spends at the bus stop is negligibly small.
a. What is the
b. What is the probability that the first bus will take more than 45 minutes to arrive?
c. What is the probability that no busses arrived from 17:00 to 17:30, but 2 busses arrived
between 17:40 and 18:10?
d. A passenger just missed the bus, what is the probability that it will take more than 30
minutes for the next bus to arrive?
e. Two types of busses service this stop (regular bus and
articulating). The probability of the arriving bus being
articulating is 1/4. Describe the time until the arrival of the
second articulated bus using am appropriate probability
function ?
f. What is the PMF for F, the number of articulating bus
arrivals between two consecutive regular bus arrivals?
g. A tourist arrives at the bus stop and wishes to observe both of the bus types. What is the
expected amount of time the tourist will spend at the bus stop to observe both types of
busses?
h. An individual arrives at the bus stop and waits for the bus. Due to their impatience, they
call a ride-share for a ride from the bus stop. The driver will arrive at a time described by
an exponentially distributed random variable with expectation of 15 minutes. What is the
probability that the bus arrived first?
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