2. You flip a fair, two-sided coin 100 times. Define a ‘run’ as a sequence of coin flips with the same value (heads or tails). for example, the sequence HTTHH has 3 runs: the first H, then the TT block, then the HH block.
Let X be the number of runs we observe in n flips. We’ve discussed how to find E(X) using indicators. Now, approximate E(X) for large n by imagining this process as a Markov Chain.