Edexcel GCE Mathematics Statistics 4 (6686) June 2008 Edexcel GCE Mark Scheme (Final) + + = 3 = 9 1 2 10 Var( θ 3 ) = 36 1 {9 σ 2 + 4 σ 2 + σ 2 } 3 4 5 µ µ µ Var( θ 1 ) = 9 θ 1 is the better estimator. It has a lower var. and no bias M1 10 1 B1,B1 Marks θ 2 is the worst estimator. It is biased A1 B1 A1 = 0 1 a = 1/3( µ − µ ) 1 { σ 2 + σ 2 + σ 2 } Var( θ 2 ) = = µ = µ E( θ 1 ) = E( θ 2 ) = E( θ 3 ) = 2 9 b σ 2 σ 2 σ 2 1 3 µ