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Unformatted text preview: ( T E = ) = p n =1 (1-p n ) . We want to know the above probability is equal to 0 or not. Sum-Product Lemma can help us for the above problem. Sum-Product Lemma : p n =1 (1-p n ) = 0 s n =1 p n = or equivalently p n =1 (1-p n ) > s n =1 p n < . Understanding Sum-Product Lemma : Let X = the number of H obtained in the sequence, I n be the indicator variable for the event that you observe H at toss n . Then X = s n =1 I n and E ( X ) = s n =1 p n . So Sum-Product Lemma tells us we can Fnally observe H if and only if we can observe H inFnite number of times. 1...
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This note was uploaded on 01/19/2011 for the course STATISTICS STAT 333 taught by Professor Menzhongxian during the Fall '10 term at Waterloo.
- Fall '10