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A coin has probability p € (0, 1) of landing on heads. The coin is tossed repeatedly. Let X be the length of the initial run: this is a run of heads if the first toss lands on heads, and a run of tails if the first toss lands on tails. Use the law of total expectation to show that E(X) 1 - 2p(1 - p) p(1 − p)

A coin has probability p € (0, 1) of landing on heads. The coin is tossed repeatedly. Let X be the length of the initial run: this is a run of heads if the first toss lands on heads, and a run of tails if the first toss lands on tails. Use the law of total expectation to show that E(X) 1 - 2p(1 - p) p(1 − p)

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.7: Probability
Problem 39E: Assume that the probability that an airplane engine will fail during a torture test is 12and that...
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A coin has probability p e (0, 1) of landing on heads. The coin is tossed repeatedly. Let X be the length of the initial run: this is a run of heads if the first toss lands on heads, and a run of tails if the first toss lands on tails. Use the law of total expectation to show that 1— 2p(1 — р) p(1 – p) - Е(X) - -
Transcribed Image Text:A coin has probability p e (0, 1) of landing on heads. The coin is tossed repeatedly. Let X be the length of the initial run: this is a run of heads if the first toss lands on heads, and a run of tails if the first toss lands on tails. Use the law of total expectation to show that 1— 2p(1 — р) p(1 – p) - Е(X) - -
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