7.118 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 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  .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.