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Unformatted text preview: N (0 , 1) by example 2 from section 5.3 so the desired probability is P (40 < X < 60) = P 4050 10 < X50 10 < 6050 10 = (1)(1) = 2(1)1 = 0 . 682 . 5.15: If Z n has a Poisson distribution with parameter = n then the limiting distribution of Y n = ( Z nn ) / n is normal with mean zero and variance 1 since lim n E h e t ( Z nn ) / n i = lim n n et n exp h n ( e t/ n1) io = lim n exp t n + n t/ n + t 2 2 n + t 3 6 n 3 / 2 = lim n exp t 2 2 + t 3 6 n 1 / 2 = exp( t 2 / 2) which is the moment generating function of N (0 , 1) . 1...
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This note was uploaded on 09/10/2009 for the course STATS 517 taught by Professor Song during the Fall '07 term at Purdue UniversityWest Lafayette.
 Fall '07
 Song
 Probability, Variance

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