In a sequence of n independent fair coin tosses, what is the expected number of occurrences of the pattern HTH (consecutively)? Note that overlap is allowed, e.g., HTHTH contains two overlapping...

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In a sequence of n independent fair coin tosses, what is the expected number of occurrences of the pattern HTH (consecutively)? Note that overlap is allowed, e.g., HTHTH contains two overlapping occurrences of the pattern.

Answered Same DayDec 26, 2021

Answer To: In a sequence of n independent fair coin tosses, what is the expected number of occurrences of the...

David answered on Dec 26 2021

124 Votes

Let X be the random variable of the total number of occurrences of "HTH" in my string of n coin
flips.
Let Xi be the indicator random variable such that "HTH" occurs for the first time in the ith
position.
Then ?(?? = 0) =
7
8
and ?(?? = 1) =
1
8

These probability values are...

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In a sequence of n independent fair coin tosses, what is the expected number of occurrences of the pattern HTH (consecutively)? Note that overlap is allowed, e.g., HTHTH contains two overlapping...

Answer To: In a sequence of n independent fair coin tosses, what is the expected number of occurrences of the...

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