Linear combinations of random variables Problem set A Answers

1. (a) \(E(Y)=39\), \(\mathrm{Var}(Y)=40\)
2. (b) \(E(Y)=-38\), \(\mathrm{Var}(Y)=62.5\)

1. (a) \(E(Z)=18\), \(\mathrm{Var}(Z)=44\)
2. (b) \(E(Z)=2.5\), \(\mathrm{Var}(Z)=4.5\)

1. (a) \(E(S)=30\), \(\mathrm{Var}(S)=8.8\)
2. (b) \(E(D)=0\), \(\mathrm{Var}(D)=4.4\)

\(E(W)=13\), \(\mathrm{Var}(W)=20.9\)

1. (a) mean 75 minutes, sd 7.35 minutes
2. (b) mean 75 minutes, sd 18 minutes
3. (c) 6

\(E(D)=10\), \(\mathrm{Var}(D)=7245\), sd = 85.1

\(a=3\), \(b=22\)

\(\mathrm{Var}(Y)=12\), \(\mathrm{Var}(3X-2Y)=93\)