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HW#5, Due 03/25
AMS 311 Probability Theory (Spring 2011)
Read: Ross, Chapter 5, Sections 5.1–5.5, 5.7. (you can skip section 5.5.1 on hazard rate
functions.)
Part 1 (10 points):
PRINT
your name and StonyBrook ID (
Last, First, #ID
) on the top on your work
sheet. Staple your HW if more than 1 pages.
Part 2: Problems (90 points)
Write down your work step by step to get full score.
(1). (10 points) Ten years ago at a certain insurance company, the size of claims under
homeowner insurance policies had an exponential distribution. Furthermore, 25% of claims were
less than $1000. Today, the size of claims still has an exponential distribution but, owing to
inflation, every claim made today is twice the size of a similar claim made 10 years ago.
Determine the probability that a claim made today is less than $1000.
(2). (15 points) In a particular forest, the distance between any randomly selected tree and the
tree nearest to it is exponentially distributed with a mean of 40 feet.
(a). Find the probability that the distance from a randomly selected tree to the tree nearest to it is
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 Spring '08
 Tucker,A
 Normal Distribution, Variance, Probability theory, Exponential distribution, flu, randomly selected tree

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