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Thinning and conditioning 2.6. EXERCISES 97 2.42. Tra c 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 10 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.
2.43. Rock concert tickets are sold at a ticket counter. Females and males arrive
at times of independent Poisson processes with rates 30 and 20 customers per
hour. (a) What is the probability the ﬁrst three customers are female? (b) If
exactly 2 customers arrived in the ﬁrst ﬁve minutes, what is the probability
both arrived in the ﬁrst three minutes. (c) Suppose that customers regardless
of sex buy 1 ticket with probability 1/2, two tickets with probability 2/5, and
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This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell University (Engineering School).
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