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Unformatted text preview: X s. 6. Derive the moment generating function for the exponential distribution with rate . Be sure to include an explantion as to why we need t < . 7. Required for 5520 students only Let X be a continuous random variable with pdf f X ( x ) and let Y = g ( X ) for some continuous invertible function g . Show that E [ g ( X )] = i - g ( x ) f X ( x ) dx. (Be sure to show the details for the limits of integration!) 8. Required for 5520 students only Let U 1 and U 2 be independent unif (0 , 1) random vari-ables. Show that X 1 and X 2 dened as X 1 = -2 ln U 1 cos(2 U 2 ) X 2 = -2 ln U 1 sin(2 U 2 ) are independent standard normal random variables....
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This note was uploaded on 02/07/2012 for the course APPM 4520 taught by Professor Manuel during the Fall '11 term at University of Colorado Denver.
- Fall '11