1. Math
  2. Statistics And Probability
  3. let x1x2xn denote independent and identically distributed random variables with...

Question: let x1x2xn denote independent and identically distributed random variables with...

Question details

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.

Solution by an expert tutor
Blurred Solution
This question has been solved
Subscribe to see this solution