Expected value flip of a coin

1. Feb 19, 2008

Somefantastik

[problem] Consider n independent flips of a coin having prob p of landing heads. Say a changeover occurs whenever an outcome differs from the one preceding it. E.g., H H T H T H H T means 5 changeovers. What is the expected number of changeovers for an arbitrary p?

[s0lution]
see attachment.

WHERE is the exponential coming from?

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2. Feb 19, 2008

EnumaElish

3. Feb 19, 2008

Somefantastik

Thank you! We haven't gotten there in class yet, so I was clueless. Thanks again.