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Unformatted text preview: E ( X ) and E ( X 2 ) : (c) Recall from handout 5, question 2 that the lifetime X (in 1000 hours) of the light bulbs that Simon bought follows an exponential distribution with & = 1 2 . 1. What is the mean lifetime of a lightbulb? 2. What is the variance of the lifetime of a lightbulb? 5. Recall that the pdf of a random variable X which follows a standard normal distribution is given by, for ²1 < x < 1 : f ( x ) = 1 p 2 ± e & x 2 = 2 : (a) Find the mgf of X . (b) Find the &rst four moments of X . [In fact, the k th moment of X is E ( X k ) = & if k is odd, 1 ³ 3 ³ 5 ³ ´´´ ³ ( k ² 1) if k is even. ] 1...
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This note was uploaded on 11/30/2011 for the course ECON 3190 at Cornell.