If 2n 1 random observations are drawn from a continuous and symmetric pdf with mean and if f Y ( ) 0, then the sample median, Y n 1 , is unbiased for , and Var(Y n 1 ) 1 (8 f Y ( ) 2 n) Show that n Y n 1 is consistent for ...

Because the symmetry of the p ...

If 2n + 1 random observations are drawn from a continuous and symmetric pdf with mean

Question:

If 2n + 1 random observations are drawn from a continuous and symmetric pdf with mean μ and if f_Y(μ; μ) = 0, then the sample median, Yʹ_n+1, is unbiased for μ, and Var(Yʹ_n+1) = 1/(8[f_Y(μ; μ)]²n) Show that ˆμ_n = Yʹ_n+1 is consistent for μ.