Let X1, X2, ..., Xn be a random sample from a normal distribution with unknown mean μ and variance 1. Let X̅ be the sample mean and X(1) = min{X1, X2, ..., Xn}. Which of the following statements are true?
1
The sample mean X̅ is an unbiased estimator of the population mean μ.
2
X(1) is also an unbiased estimator of the population mean μ
3
The distribution of the sample mean X̅ is also a normal distribution with mean μ and variance 1/n.
4
The expected value of X(1) is equal to the population mean μ.