Question

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 ybe the length (number of trials) in the longest run of S's. (Round your answers to four decimal places.)

(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).

y	p(y)
0
1
2
3
4

Calculate μ_y.
μ_y =  

(b) Repeat Part (a) for the case p = 0.7.

y	p(y)
0
1
2
3
4

Calculate μ_y.
μ_y =  

(c) Let z denote the longest run of either S's or F's. Determine the probability distribution of z when p = 0.5.

z	p(z)
1
2
3
4

Answer 1