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]?

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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$, that is W100 = 11. What is your expected wealth if
you do another 100 tosses, that is E[W200|W100 = 11]?
Transcribed Image Text:5. Suppose you are tossing a fair coin to bet. At each time your gain is Xi. The rule is: (0) if you get heads at i-th toss, Xi = 1$; (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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