3. (Competing patterns among coin flips) Suppose that Xn, n > 1 are i.i.d. random variables with P(X1 = 1) = P(X1 = 0) =

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3. (Competing patterns among coin flips) Suppose that Xn, n > 1 are i.i.d. random variables with P(X1 = 1) = P(X1 = 0) =

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3 Competing Patterns Among Coin Flips Suppose That Xn N 1 Are I I D Random Variables With P X1 1 P X1 0 1
3 Competing Patterns Among Coin Flips Suppose That Xn N 1 Are I I D Random Variables With P X1 1 P X1 0 1 (85.11 KiB) Viewed 18 times
3. (Competing patterns among coin flips) Suppose that Xn, n > 1 are i.i.d. random variables with P(X1 = 1) = P(X1 = 0) = Ž. (These are just i.i.d. fair coin flips.) Let = 1 2 A= (a1, 22, a3) = (0,1,1), B = (b1,b2, 63) = (0,0,1). = = : = , -2 Let Ta = min(n > 3:{Xn-2, Xn-1, Xn) = A} be the first time we see the sequence A appear among the Xn random variables, and define TB similarly for B. Find the probability that P(TA <TB). (This is the probability that THH shows up before TTH in a sequence of fair coin flips.)
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