chapter 1

Chapter 3: Discrete Random Variables and Probability Distributions18.1a. p(1) = P(M = 1 ) = P[(1,1)] = 363p(2) = P(M = 2 ) = P[(1,2) or (2,1) or (2,2)] = 365p(3) = P(M = 3 ) = P[(1,3) or (2,3) or (3,1) or (3,2) or (3,3)] = 36Similarly, p(4) = 7 36, p(5) = 9 1136, and p(6) = 361b. F(m) = 0 for m < 1, 36for 1 ≤ m < 2,F(m) =⎧ 0⎪ 1⎪ 36⎪436⎪9⎨ 36⎪16⎪3625⎪36⎪⎩ 1m < 11 ≤ m < 22 ≤ m < 33 ≤ m < 44 ≤ m < 55 ≤ m < 6m ≥ 61.00.90.80.70.60.50.40.30.20.10.001234567819. Let A denote the type O+ individual ( type O positive blood) and B, C, D, the other 31individuals. Then p(1) – P(Y = 1) = P(A first) = 4= .25p(2) = P(Y = 2) = P(B, C, or D first and A next) = 3 1 1⋅ = = . 25p(4) = P(Y = 3) = P(A last) = 3 2 1 1⋅ ⋅ = = . 25So p(3) = 1 – (.25+.25+.25) = .25432443420. P(0) = P(Y = 0) = P(both arrive on Wed.) = (.3)(.3) = .09P(1) = P(Y = 1) = P[(W,Th)or(Th,W)or(Th,Th)]= (.3)(.4) + (.4)(.3) + (.4)(.4) = .40P(2) = P(Y = 2) = P[(W,F)or(Th,F)or(F,W) or (F,Th) or (F,F)] = .32P(3) = 1 – [.09 + .40 + .32] = .19100