chapter 1

Chapter 3: Discrete Random Variables and Probability DistributionsSection 3.675.a. P(X ≤ 8) = F(8;5) = .932b. P(X = 8) = F(8;5) - F(7;5) = .065c. P(X ≥ 9) = 1 – P(X ≤ 8) = .068d. P(5 ≤ X ≤ 8) = F(8;5) – F(4;5) = .492e. P(5 < X < 8) = F(7;5) – F(5;5) = .867-.616=.25176.a. P(X ≤ 5) = F(5;8) = .191b. P(6 ≤ X ≤ 9) = F(9;8) – F(5;8) = .526c. P(X ≥ 10) = 1 – P(X ≤ 9) = .283d. E(X) = λ= 10, σ X = = 2. 83.936 = .064λ , so P(X > 12.83) = P(X ≥ 13) = 1 – P(X ≤ 12) =1 -77.a. P(X ≤ 10) = F(10;20) = .011b. P(X > 20) = 1 – F(20;20) = 1 - .559 = .441c. P(10 ≤ X ≤ 20) = F(20;20) – F(9;20) = .559 - .005 = .554P(10 < X < 20) = F(19;20) – F(10;20) = .470 - .011 = .459d. E(X) = λ= 20, σ X = λ = 4. 472P(µ - 2σ < X < µ + 2σ ) = P(20 – 8.944 < X < 20 + 8.944)= P(11.056 < X < 28.944)= P(X ≤ 28) - P(X ≤ 11)= F(28;20) - F(12;20)]= .966 - .021 = .94578.a. P(X = 1) = F(1;2) – F(0;2) = .982 - .819 = .163b. P(X ≥ 2) = 1 – P(X ≤ 1) = 1 – F(1;2) = 1 - .982 = .018c. P(1 st doesn’t ∩ 2 nd doesn’t) = P(1 st doesn’t) ⋅ P(2 nd doesn’t)= (.819)(.819) = .671118