Suppose that n 5 observations are taken from the uniform pdf, fY (y ) 1 , 0 y , where is unknown Two unbiased estimators for are 1 6 5Y max and 2 6Y min Which estimator would be better to use What must be true of Var(Y max ) and Var(Y min ) given that f Y (y ) is symmetric Does your answer as to wh...

From the solution to Question 542 By symmetry VarY min Va ...

Suppose that n = 5 observations are taken from the uniform pdf, fY (y; ) = 1/,

Question:

Suppose that n = 5 observations are taken from the uniform pdf, fY (y; θ) = 1/θ, 0 ≤ y ≤ θ, where θ is unknown. Two unbiased estimators for θ are ˆθ₁ = 6/5・Y_max and ˆθ₂ = 6・Y_min

Which estimator would be better to use? [What must be true of Var(Y_max) and Var(Y_min) given that f_Y(y; θ) is symmetric?] Does your answer as to which estimator is better make sense on intuitive grounds? Explain.