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Unformatted text preview: Proper random variables can be further classiFed into two types: Short proper waiting times: E ( X ) < Null (long) waiting times: E ( X ) = Infnite Sums and Infnite Products: By deFnition s k =1 a k = lim n n s k =1 a k and p k =1 a k = lim n n p k =1 a k The Sum-Product Lemma: Suppose 0 < a n < 1 for each n . Then p k =1 (1-a k ) > if and only if s k =1 a k < A Lower Bound In The Geometric Case: Suppose 0 < p < 1 / 2 and a k = p k . Then p k =1 (1-p k ) 1- s k =1 p k = 1-p 1-p = 1-2 p 1-p...
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This note was uploaded on 07/12/2010 for the course STAT 333 taught by Professor Chisholm during the Winter '08 term at Waterloo.
- Winter '08