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The longest "run" of S's in the sequence SSFSSSSFFS has length 4, corresponding to the S's on the fourth, fifth, sixth, and seventh positions. Consider a binomial experiment with n = 4, and let y be the length in the longest run of S's.
a. When p = .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 my.
b. Repeat Part (a) for the case p = .6.
c. Let z denote the longest run of either S's or F's. Determine the probability distribution of z when p = .5.
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