The longest “run” of S’s in the 10 trial sequence SSFSSSSFFS has length 4, corresponding to the S’s on the fourth, fifth, sixth, and seventh trials. Consider a binomial experiment with n = 4, and let y be the length (number of trials) in the longest run of S’s.
a. When p = 0.5, the 16 possible outcomes are equally likely. Determine the probability distribution of y in this case (first list all outcomes and the y value for each one). Then calculate µ y.
b. Repeat Part (a) for the case p = 0.6.