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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- Fall '10
- Probability, Probability theory, Sum-Product Lemma