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(a) A fair coin is tossed repeatedly and independently until two consecutive heads or two consecutive tails appear. Find the PMF, the expected value, and the variance of the number of tosses.
(b) Assume now that the coin is tossed until we obtain a tail that is immediately preceded by a head. Find the PMF and the expected value of the number of tosses.
Verified Expert
This task provides a clear working example of probability mass function. The experiment uses flipping a coin until consecutive head or tail turns up. This experiment is an example of discrete probability distribution and therefore, random walk concept using markov chain should be applied.
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