If Y 1 , Y 2 , , Y n are random observations from a uniform pdf over 0, , both 1 (n 1 n)Y max and 2 (n 1) Y min are unbiased estimators for Show that Var( 2 ) Var( 1 ) n 2

Question: If Y 1 , Y 2 , . . . , Y n are random observations from a uniform pdf over [0, ], both

If Y₁, Y₂, . . . , Y_n are random observations from a uniform pdf over [0, θ], both ˆθ₁ = (n + 1/n)・Y_max and ˆθ₂ = (n + 1). Y_min are unbiased estimators for θ. Show that Var(ˆθ₂)/Var(ˆθ₁) = n₂.

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