Unformatted text preview: (b) Find (approximately) the largest value of n such that P ( X 1 + Â·Â·Â· + X n â‰¥ 200 + 5 n ) â‰¤ . 05 . (c) Let N be the Â±rst day on which the total number of gadgets produced exceeds 1000. Calculate an approximation to the probability that N â‰¥ 220. 3. Let X 1 ,X 2 ,..., be independent Poisson random variables with mean and variance equal to 1. For any n > 0, let S n = âˆ‘ n i =1 X i . (a) Show that S n is Poisson with mean and variance equal to n . Hint: Relate X 1 ,X 2 ,...,X n to a Poisson process with rate 1. (b) Show how the central limit theorem suggests the approximation n ! â‰ˆ âˆš 2 Ï€n p n e P n for large values of the positive integer n . Page 1 of 1...
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This note was uploaded on 12/02/2011 for the course ENGINEERIN EE302 taught by Professor Proasin during the Spring '11 term at South Carolina.
 Spring '11
 Proasin
 Computer Science, Electrical Engineering

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