Question: Let X 1 , X 2 , X 3 , . . ., X n be a random sample from the following distribution where

Let X1, X2, X3, . . ., Xn be a random sample from the following distributionfx(x) = Jo (x - 2) 0 +1 for 0x 1 otherwise

where θ ∈ [−2, 2] is an unknown parameter. We define the estimator ^Θn asn =12X 6

to estimate θ.

a. Is ^Θn an unbiased estimator of θ?

b. Is ^Θn a consistent estimator of θ?

c. Find the mean squared error (MSE) of ^Θn.

fx(x) = Jo (x - 2) 0 +1 for 0x 1 otherwise

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