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Unformatted text preview: AMS 311 (Fall, 2010) Joe Mitchell PROBABILITY THEORY Homework Set # 5 Due at the beginning of class on Thursday, October 28, 2008. Reminder: Show your reasoning! Read: Ross, Chapter 5, Sections 5.1–5.5, 5.7. (You may skip section 5.5.1 on hazard rate functions.) (1). (15 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 more than 30 feet. (b). Find the probability that the distance from aselected tree to the tree nearest to it is more than 30 feet....
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This note was uploaded on 07/15/2011 for the course AMS 311 taught by Professor Tucker,a during the Spring '08 term at SUNY Stony Brook.
- Spring '08