20101ee131A_1_hwk-2-ee131-A-09

20101ee131A_1_hwk-2-ee131-A-09 - Problem 3: An insurance...

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Homework 2 Problem 1: An urn contains r Red balls and w white balls. An experiment consists of picking two balls, sequentially and without replacement , and noting the color of the ball for each pick. Let us de ne the following events: W 1 : The rst pick is a White ball; R 1 : The rst pick is a Red ball; W 2 : The second pick is a White ball; and R 2 : The second pick is a Red ball. 1. Compute the probabilities: P [ W 1 and W 2 ] , P [ R 1 and W 2 ] , P [ W 1 and R 2 ] , and P [ R 1 and R 2 ] 2. Compute the probabilities P [ W 2 ] and P [ R 2 ] , and show that they equal P [ W 1 ] and P [ R 1 ] , respectively. 3. Show that P [ W 1 | W 2 ] = P [ W 2 | W 1 ] and compute P [ R 1 | W 2 ] . Problem 2: A bin contains 25 lightbulbs, 5 of which are in good condition and will function for at least thirty days, 10 of which are partially defective and will fail in their second day of use, and 10 of which are totally defective and will not light up at all. Given that a randomly chosen bulb initially lights, what is the probability it will still be working after one week?
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Unformatted text preview: Problem 3: An insurance company believes that people can be divided into two classes: those who are accident prone and those who are not. Their statistics show that an accident-prone person will have an accident at some time within a xed 1-year period with probability . 4 , whereas this probability decreases to . 2 for a non-accident-prone person. 1. If we assume that 30 percent of the population is accident prone, what is the probability that a new policyholder will have an accident within a year of purchasing a policy? 2. Suppose that a new policyholder has an accident within a year of purchasing a policy. What is the probability that he or she is accident prone? Problems 4-8: The following problems from Chapter 2 of the text book: 2.62, 2.69, 2.73, 2.75, 2.79...
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This note was uploaded on 09/28/2010 for the course EE 131A EE 131A taught by Professor Vwaniroychowdhury during the Winter '10 term at UCLA.

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