How Do You Calculate the Expected Number of Changeovers in Coin Flips?

[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?

 

[EnumaElish]

E[e^(tX)] is the moment-generating function.

 

[Somefantastik]

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