IE 111 Fall 2011
Homework Assignment #7
Due Monday October 31
Question 1.
The total amount of snow during a winter in the Lehigh valley is a random variable with
mean 40 inches and variance 100 inches.
My son is wishing for 100 or more inches of
snow this winter.
What can you tell him about the probability of his wish?
Question 2.
On Tuesdays, patients arrive to the hospital at a rate of 2.5 per hour according to a
Poisson process.
I work an 8 hour shift at the hospital.
a)
Find the probability that exactly 20 patients arrive during my shift.
b)
Find the probability that 20 or fewer patients arrive during my shift.
c)
Find the probability that 10 or more patients arrive during my shift.
d)
On Mondays the patient arrival rate is 1.5 patients per hour (rather than 2.5 as on
Tuesdays).
Let X be the total number of patients that arrive during my shift on
Monday and Tuesday.
Find the expected value of X.
Question 3.
Street lights in a certain city burn out according to a Poisson process with rate 6 per day.
What is the probability that 50 or more burn out in a week?
Question 4.
Forest fires in the state of Wyoming occur according to a Poisson process with rate 2 per
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 Fall '07
 Storer
 Probability, japan, Probability theory, Poisson process

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