chapter 1

Chapter 3: Discrete Random Variables and Probability DistributionsSection 3.444.a. b(3;8,.6) =b. b(5;8,.6) =⎛8⎞⎜ ⎟(.6)⎝3⎠⎛8⎞⎜ ⎟(.6)⎝5⎠35(.4)(.4)53= (56)(.00221184) = .124= (56)(.00497664) = .279c. P( 3 ≤ X ≤ 5) = b(3;8,.6) + b(4;8,.6) + b(5;8,.6) = .635d. P(1 ≤ X) = 1 – P(X = 0 ) = 1 -⎛12⎞⎜ ⎟(.1)⎝ 0 ⎠0(.9)12= 1 – (.9) 12 = .71845.a. B(4;10,.3) = .850b. b(4;10,.3) = B(4;10,.3) - B(3;10,.3) = .200c. b(6;10,.7) = B(6;10,.7) - B(5;10,.7) = .200d. P( 2 ≤ X ≤ 4) = B(4;10,.3) - B(1;10,.3) = .701e. P(2 < X) = 1 - P(X ≤ 1) = 1 - B(1;10,.3) = .851f. P(X ≤ 1) = B(1;10,.7) = .0000g. P(2 < X < 6) = P( 3 ≤ X ≤ 5) = B(5;10,.3) - B(2;10,.3) = .57046. X ~ Bin(25, .05)a. P(X ≤ 2) = B(2;25,.05) = .873b. P(X ≥ 5) = 1 - P(X ≤ 4) = 1 – B(4;25,.05) = .1 - .993 = .007c. P( 1 ≤ X ≤ 4) = P(X ≤ 4) – P(X ≤ 0) = .993 - .277 = .716d. P(X = 0) = P(X ≤ 0) = .277e. E(X) = np = (25)(.05) = 1.25V(X) = np(1 – p) = (25)(.05)(.95) =1.1875σ x = 1.0897107