Question: Please provide clear explanation and show your steps. Thank you! 8. More Coin Flipping (10 points) A coin with probability p of coming up heads

Please provide clear explanation and show your steps. Thank you!

8. More Coin Flipping (10 points) A coin with probability p of coming up heads is tossed independently n times. What is the expected number of maximal "runs", where a "run" is a maximal sequence of consecutive flips that are the same? For example, the sequence HHHTTHTHHH has 5 runs, the first three H, the following two T, and so on. Use linearity of expectation and carefully define indicator rvs and justify your work

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