Exercise. Let (Sn)n>o be a biased random walk started from 0. That is, n Sn = $k k=1 where (Ek) k>1 is a sequence of ind

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Exercise Let Sn N O Be A Biased Random Walk Started From 0 That Is N Sn K K 1 Where Ek K 1 Is A Sequence Of Ind 1 (20.88 KiB) Viewed 20 times

Exercise. Let (Sn)n>o be a biased random walk started from 0. That is, n Sn = $k k=1 where (Ek) k>1 is a sequence of independent, identically distributed ran- dom variables with P(₁ = 1) = p = 1 - P(₁ = -1) for p > 1/2. Use the strong law of large numbers to show that T = sup{n> 0: Sn=0} is almost surely finite.