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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).