Suppose you are tossing a fair coin to bet. At each time your gain is Xi. The rule is: () if you get heads at i-th toss, Xị = 1$; (ii) if you get tails at i-th toss, X; = -1$. Let Wn = X1+ X2 ++ Xn with Wo = 0. Note that Wn represents your total wealth after n tosses. Suppose after 100 tosses you have 11$, that is W100 = 11. What is your expected wealth if you do another 100 tosses, that is E[W200|W100 = 11]?
Suppose you are tossing a fair coin to bet. At each time your gain is Xi. The rule is: () if you get heads at i-th toss, Xị = 1$; (ii) if you get tails at i-th toss, X; = -1$. Let Wn = X1+ X2 ++ Xn with Wo = 0. Note that Wn represents your total wealth after n tosses. Suppose after 100 tosses you have 11$, that is W100 = 11. What is your expected wealth if you do another 100 tosses, that is E[W200|W100 = 11]?
Chapter9: Sequences, Probability And Counting Theory
Section9.5: Counting Principles
Problem 42SE: In horse racing, a “trifecta” occurs when a bettor wins by selecting the first three finishers in...
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![5. Suppose you are tossing a fair coin to bet. At each time your gain is Xi. The rule is: (0) if
you get heads at i-th toss, Xi = 1$; (ii) if you get tails at i-th toss, Xi = -1$. Let Wn =
X1+ X2 + .+ Xn with Wo = 0. Note that Wn represents your total wealth after n tosses.
Suppose after 100 tosses you have 11$, that is W100 = 11. What is your expected wealth if
you do another 100 tosses, that is E[W200|W100 = 11]?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F815f2e5b-f4d0-4ba3-88d9-27b4d72d9abe%2Fb58ef610-5639-4474-827b-b7af1be354ba%2Fpu1cmqp_processed.png&w=3840&q=75)
Transcribed Image Text:5. Suppose you are tossing a fair coin to bet. At each time your gain is Xi. The rule is: (0) if
you get heads at i-th toss, Xi = 1$; (ii) if you get tails at i-th toss, Xi = -1$. Let Wn =
X1+ X2 + .+ Xn with Wo = 0. Note that Wn represents your total wealth after n tosses.
Suppose after 100 tosses you have 11$, that is W100 = 11. What is your expected wealth if
you do another 100 tosses, that is E[W200|W100 = 11]?
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