3. (Competing patterns among coin flips) Suppose that Xn,n > 1 are i.i.d. random variables with P(X1 = 1) = P(X1 = 0) = }. (These are just i.i.d. fair coin flips.) Let = (a1, a2, a3) = (0, 1,1), В - = (b1, b2, b3) = (0,0, 1). Let TA = min(n > 3: {Xn-2, Xn-1, Xn) = A} be the first time we see the s 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.) sequence A аppear

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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) = }. (These are just i.i.d. fair coin flips.) Let
A = (a1, a2, a3) = (0, 1, 1),
B = (b1, b2, b3) = (0,0, 1).
Let TA = min(n 2 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.)
Transcribed Image Text:3. (Competing patterns among coin flips) Suppose that Xn, n > 1 are i.i.d. random variables with P(X1 = 1) = P(X1 = 0) = }. (These are just i.i.d. fair coin flips.) Let A = (a1, a2, a3) = (0, 1, 1), B = (b1, b2, b3) = (0,0, 1). Let TA = min(n 2 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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