i.i.d. Let X1,..., Xn Poisson(A) and let A = E, X; = Xn. Find the bias, stan- (a) dard error (SE), and mean squared error (MSE) of A. Is X consistent? Prove/disprove n Li=1 it. i.i.d. Let X1,..., Xn Uniform[0, 0] and let ô = 2X,m. Find the bias, standard error (b) (SE), and mean squared error (MSE) of 0. Is 0 consistent? Prove/disprove it. Hint: For proving consistency, it is often useful to invoke the law of large numbers (LLN).

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Author:Amos Gilat
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Question
i.i.d.
(a)
Let X1, ..., Xn
Poisson(A) and let A= !E X; = Xn. Find the bias, stan-
n
dard error (SE), and mean squared error (MSE) of A. Is consistent? Prove/disprove
it.
i.i.d.
Let X1,..., Xn
Uniform[0, 0] and let 0 = 2X. Find the bias, standard error
(b)
(SE), and mean squared error (MSE) of 0. Is 0 consistent? Prove/disprove it.
Hint: For proving consistency, it is often useful to invoke the law of large numbers (LLN).
Transcribed Image Text:i.i.d. (a) Let X1, ..., Xn Poisson(A) and let A= !E X; = Xn. Find the bias, stan- n dard error (SE), and mean squared error (MSE) of A. Is consistent? Prove/disprove it. i.i.d. Let X1,..., Xn Uniform[0, 0] and let 0 = 2X. Find the bias, standard error (b) (SE), and mean squared error (MSE) of 0. Is 0 consistent? Prove/disprove it. Hint: For proving consistency, it is often useful to invoke the law of large numbers (LLN).
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