Chun flips a fair coin until the first time she sees the either one of the sequences HH or HTT. (a) Explain why the experiment ends in a finite time with probability 1. (b) The first three outcomes were TTT. Construct a Markov chain and use it to calculate the probabil- ity that Chun sees HH before HTT. Hint: Consider all the possible 8 states (HHH, HHT,....TTT}; or, alternatively, the following five states: (1) HH was obtained before HTT; (2) HTT was obtained before HH; (3) neither HH nor HTT occurred already, and the last letter is H; (4) neither HH nor HTT occurred already, and the last two letters are HT; (5) neither HH nor HTT occurred already, and the last two letters are TT. (c) Find the expected time until hitting either HH or HTT. Do not include the first three flips that showed TTT.
Chun flips a fair coin until the first time she sees the either one of the sequences HH or HTT. (a) Explain why the experiment ends in a finite time with probability 1. (b) The first three outcomes were TTT. Construct a Markov chain and use it to calculate the probabil- ity that Chun sees HH before HTT. Hint: Consider all the possible 8 states (HHH, HHT,....TTT}; or, alternatively, the following five states: (1) HH was obtained before HTT; (2) HTT was obtained before HH; (3) neither HH nor HTT occurred already, and the last letter is H; (4) neither HH nor HTT occurred already, and the last two letters are HT; (5) neither HH nor HTT occurred already, and the last two letters are TT. (c) Find the expected time until hitting either HH or HTT. Do not include the first three flips that showed TTT.
A First Course in Probability (10th Edition)
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ISBN:9780134753119
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Chapter1: Combinatorial Analysis
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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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Transcribed Image Text:Chun flips a fair coin until the first time she sees the either one of the sequences HH or HTT.
(a) Explain why the experiment ends in a finite time with probability 1.
(b) The first three outcomes were TTT. Construct a Markov chain and use it to calculate the probabil-
ity that Chun sees HH before HTT. Hint: Consider all the possible 8 states {HHH, HHT, ...,TTT};
or, alternatively, the following five states:
(1) HH was obtained before HTT;
(2) HTT was obtained before HH;
(3) neither HH nor HTT occurred already, and the last letter is H;
(4) neither HH nor HTT occurred already, and the last two letters are HT;
(5) neither HH nor HTT occurred already, and the last two letters are TT.
(c) Find the expected time until hitting either HH or HTT. Do not include the first three flips that
showed TTT.
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