Flip a fair coin n times. using markov's and
chebyshev'sinequalities ,prove that the length of the longest
constant run inthe resulting list of heads and tails is (1 +
o(1))log_{2}(n). inother words, for every a> 0, almost no list
has at least(1+a)log_{2}(n) consecutive identical flips, and almost
every listhas at least (1-a)log_{2}(n) consecutive identical
flips.