초록
It is well-known that the sample mean and the sample variance are jointly sufficient under normality assumption. In this paper a proof of the joint sufficiency is given without using the factorization criterion. It is related to a finite Sanov-type conditional theorem, i.e., the conditional probability density of $Y_1$ given sample mean $\mu$ and sample variance $\sigma^2$, where $Y_1, Y_2, \cdots, Y_n$ are independently and identically distributed (i.i.d.) normal random variables with mean m and variance $\delta^2$, equals that of $Y_1$ given sample mean $\mu$ and sample variance $\sigma^2$, where $Y_1, Y_2, \cdots, Y_n$ are i.i.d. normal random variables with mean $\mu$ and variance $\sigma^2$.