Normal Distribution (Casella, G. & Berger, 2nd ed.)

Combinatorics · Casella, G. & Berger, 2nd ed. | proposed by @Ale712 1208

Suppose $X_1,\ldots,X_n$ are independent and identically distributed from a normal distribution $N(\mu,\sigma^{2})$. Which of the following statements is true?

AThe Sample mean $\bar{X}$ and sample variance $S^{2}$ are always independent for any underlying ditribution. B$\bar{X}$ and $S^{2}$ are independent specifically because the population is normal. C$\bar{X}$ and $S^{2}$ are uncorrelated but never independent. DTheir independence requires $\mu=0$.