Suppose we have a random sample of size 2n from a

QUESTION:

Suppose we have a random sample of size 2n from a population denoted by X, and \(E(X)=\mu\) and \(V(X)=\sigma^{2}\). Let

                       \(\bar{X}_{1}=\frac{1}{2 n} \sum_{i=1}^{2 n} X_{i} \quad \text { and } \quad \bar{X}_{2}=\frac{1}{n} \sum_{i=1}^{n} X_{i}\)

be two estimators of \(\mu\). Which is the better estimator of \(\mu\)? Explain your choice.

Equation Transcription:

Text Transcription:

E(X)=mu

V(X)=sigma^2

X bar_1=1 over 2n sum i=1 2n X_i   and   X bar_2=1 over n sum i=1 n X_i

mu

mu