Sign in to jmaths to print this page or save it as a PDF: jmaths-8ce638778fd6.herokuapp.com/maths/ai-hl/statistics-2/ahl-8-4/problems/b/

jmaths

IB Mathematics: Applications and Interpretation HL · AHL 8: Statistics 2 · AHL 8.4

Linear combinations of random variables Problem set B Answers

Skills

    1. (a) \(E(Y)=33.4\), \(\mathrm{Var}(Y)=57.6\)
    2. (b) \(E(Y)=-10.2\), \(\mathrm{Var}(Y)=14.4\)
    1. (a) \(E(Z)=38\), \(\mathrm{Var}(Z)=83\)
    2. (b) \(E(Z)=8.25\), \(\mathrm{Var}(Z)=3\)
    1. (a) \(E(S)=4\), \(\mathrm{Var}(S)=1.75\)
    2. (b) \(E(D)=0\), \(\mathrm{Var}(D)=0.7\)

  4. \(E(W)=29\), \(\mathrm{Var}(W)=13.9\)

In context

    1. (a) mean 2560 g, sd 30 g
    2. (b) mean 2560 g, sd 60 g
    3. (c) 4

  2. \(E(D)=-38\), \(\mathrm{Var}(D)=101.5\), sd = 10.1

Stretch

  1. \(a=4\), \(b=-7\)

  2. \(\mathrm{Var}(Q)=14\), \(\mathrm{Var}(2P-5Q)=374\)

jmaths.xyz · AI HL · AHL 8.4 Linear combinations of random variables