Question

Let X1,X2,...,Xn denote independent and identically distributed random variables with mean µ and variance 2. State whether each of the following statements are true or false, fully justifying your answer.

(a) T =(n/n-1)X is a consistent estimator of µ.

(b) T = $\frac{1}{3}(X_{2}+X_{5}+X_{n-1})$ is a consistent estimator of µ (assuming n7).

(c) T = $\frac{1}{n}(\sum_{I=1}^{n}(X_{i}-2))+3$ is an unbiased estimator of µ.

(d) T = X1X2 is an unbiased estimator of µ^2.

Answer 1

Solution: Letx,厂ッxn be iidTVs with bias f js Vaiahye both tends to zey as h 上2 X n-1 2 )2 N(T NCT) is hd fends to zero

T= h(..'rL(Xǐー2.) )+3 E(r)二方向 e).le( nd,U-243 ECT)1 +( T IS no ie. False e. This stafe meh! is hue Sa, a, b, c are false starlement d is hue ten.