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# HW5 - HW#5 Due 03/25 AMS 311 Probability Theory(Spring 2011...

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6 3 5 3 2 1 4 2 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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HW5 - HW#5 Due 03/25 AMS 311 Probability Theory(Spring 2011...

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