Solutions HWB08

6.10:

For each toss, mu = pi = .5 and sigma = sqrt[(pi)(1-pi)] = .5

For n = 100 tosses, mu = n(pi) = 50, sigma = sqrt[n(pi)(1-pi)] = 5.

For n = 400 tosses, mu = n(pi) = 200, sigma = sqrt[n(pi)(1-pi)] = 10.

6.12: Here pi = .25 and n = 5.

6.12a: Pr(K = 1) = (5)(.25^1)(.75^4) = .3955

6.12a: Pr(K = 3) = (10)(.25^3)(.75^2) = .0879

6.12a: Pr(K > 2) = Pr(K = 3) + Pr(K = 4) + Pr(K = 5) = .0879 +.0146 + .0010 = .1035

6.12a: Pr(at least one wrong) = 1 – Pr(all correct) = 1 - Pr(K = 5) = 1 - (1)(.25^5)(.75^0) = .9990