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...

3. (Competing patterns among coin flips) Suppose that Xn, n > 1 are i.i.d. random variables<br>with P(X1 = 1) = P(X1 = 0) = }. (These are just i.i.d. fair coin flips.) Let<br>A = (a1, a2, a3) = (0, 1, 1),<br>B = (b1, b2, b3) = (0,0, 1).<br>Let TA = min(n 2 3: {Xn-2, Xn-1, Xn) = A} be the first time we see the sequence A appear<br>among the Xn random variables, and define TB similarly for B. Find the probability that<br>P(TA < TB).<br>(This is the probability that THH shows up before TTH in a sequence of fair coin flips.)<br>

Extracted 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="">

Jun 01, 2022

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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...

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