319handout9 - be a random variable that is uniformly...

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Econ 319, Fall 2008 TA: Simon Kwok Handout 9 1. Suppose that on a certain examination in advanced mathematics, students from college A achieve scores which are normally distributed with a mean of 625 and a variance of 100, and students from college B achieve scores which are normally distributed with a mean of 600 and a variance of 150. The scores of all students are independent. (a) What is the probability that the scores a student from college A will be higher than 630? (b) Suppose two students from college A take this exam. What is the probability that the average of the scores of the two students from college A will be higher than 630? (c) Suppose two students from college A and three students from college B take this exam. What is the probability that the average of the scores of the two students from college A will be higher than the average of the scores of the three students from college B? 2. Suppose that T has a t distribution with v degrees of freedom. What is the distribution of X = T 2 ? 3. Let X
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Unformatted text preview: be a random variable that is uniformly distributed on the interval [-1,1]. Derive the cumulative distribution function (cdf) and pdf of (a) Y = log( X + 1) , (b) Y = j X j , and (c) Y = X 2 (d) Y = X 3 . Be sure to give the support of Y in each case. Verify by integration that each of these pdfs actually integrates to 1. 4. Recall from handout 5, question 2 that the lifetime X (in 1000 hours) of the light bulbs (let&s call it brand A) that Simon bought follows an exponential distribution with & = 1 2 . Suppose now that there is another brand of lightbulbs (call it brand B) whose lifetime (again in 1000 hours) is distributed according to Y = p 2 X . (a) Find the cdf and pdf of the lifetime of brand B lightbulbs. (b) An advertisement claims that brand B lightbulbs are more durable than brand A light-bulbs on average. Do you agree? [Part (b) is for those who are interested. Look for "Weibull distribution" from Wikipedia, for instance, to obtain E ( Y ) : ] 1...
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This note was uploaded on 11/30/2011 for the course ECON 3190 at Cornell University (Engineering School).

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