Great Expectations: Part 1
1. Introduction HHTTTHHHHHHTTTTHHTTHHHTHHHTHTTHHHTTTHHHHTTHTHHTTHH Displayed above is the result of consecutive random coin flips. In total there are 29 heads and 21 tails, not too outlandish given our relatively small sample size. We can ask several interesting questions about strings of random coin flips like the one above, and I was working on a mathematical research project recently when I encountered one such problem: Given a string of independent flips of a fair coin, what is the expected length of the…