Unformatted text preview: x = 0 (fall) or x = 10 (survival). What is the probability that the particle eventually survives? 4. Problem. Consider the following symmetric random walk with no barriers. A particle starts at x = 0. With probability 1 / 2 the particle moves one step to the right and with probability 1 / 2 the particle moves one step to the left. Prove that the probability that the particle returns to x = 0 for the Frst time after 2 n steps is 1 2 n1 p 2 n n P 22 n . 5. Problem. a) We toss a fair coin n times. Let a n be the number of outcomes which do not contain a sequence . . .HTH . . . and for which the Frst toss lands H and let b n be the number of outcomes which do not contain a sequence . . .HTH . . . and for which the Frst toss lands T . ±ind a recurrence formula relating numbers a n and b n . b) We toss a fair coin 10 times. What is the probability that there will be a sequence . . .HTH . . . ? 1...
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 Winter '12
 AlexanderBarvinok
 Probability, Rightwing politics, Leftwing politics, Political spectrum, Gaming mathematics

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