Unformatted text preview: N (0 , 1) by example 2 from section 5.3 so the desired probability is P (40 < X < 60) = P Â± 4050 10 < X50 10 < 6050 10 Â¶ = Î¦(1)Î¦(1) = 2Î¦(1)1 = 0 . 682 . 5.15: If Z n has a Poisson distribution with parameter Î¼ = n then the limiting distribution of Y n = ( Z nn ) / âˆš n is normal with mean zero and variance 1 since lim n â†’âˆž E h e t ( Z nn ) / âˆš n i = lim n â†’âˆž n et âˆš n exp h n ( e t/ âˆš n1) io = lim n â†’âˆž â€° exp â€¢t âˆš n + n Â± t/ âˆš n + t 2 2 n + t 3 6 n 3 / 2 Â·Â·Â· Â¶â€šÂ² = lim n â†’âˆž â€° exp Â± t 2 2 + t 3 6 n 1 / 2 Â·Â·Â· Â¶Â² = exp( t 2 / 2) which is the moment generating function of N (0 , 1) . 1...
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 Fall '07
 Song
 Probability, Variance, Probability theory, lim P, MATHEMATICAL PROBABILITY ASSIGNMENT, lim E et

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