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 First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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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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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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