The sample mean and its standard error Problem set A Answers

1. (a) \(E(\bar{X})=7.5\), \(\mathrm{Var}(\bar{X})=0.3\)
2. (b) \(E(\bar{X})=-12.6\), \(\mathrm{Var}(\bar{X})=0.045\)

1. (a) \(E(\bar{X})=20\), \(\mathrm{Var}(\bar{X})=2\)
2. (b) \(E(\bar{X})=5.5\), \(\mathrm{Var}(\bar{X})=0.024\)

1. (a) \(E(X)=4, \mathrm{Var}(X)=2.4\); \(E(\bar{X})=4\), \(\mathrm{Var}(\bar{X})=0.2\)
2. (b) \(E(X)=5, \mathrm{Var}(X)=4\); \(E(\bar{X})=5\), \(\mathrm{Var}(\bar{X})=0.4\)

1. (a) 1.6
2. (b) 6
3. (c) 21

1. (a) 0.5
2. (b) 2
3. (c) 72

1. (a) \(E(\bar{X})=1.02\), \(\mathrm{Var}(\bar{X})=0.000064\)
2. (b) 0.008 kg
3. (c) 0.004 kg; the standard error halves

1. (a) \(E(X)=4, \mathrm{Var}(X)=3.68\)
2. (b) \(E(\bar{X})=4\), \(\mathrm{Var}(\bar{X})=0.123\)

1. (a) \(E(\bar{X})=32\), \(\mathrm{Var}(\bar{X})=1.8\)
2. (b) 1.34 minutes

\(E(\bar{C})=138\), \(\mathrm{Var}(\bar{C})=81\), SE = 9