題組內容

1.5. (10%) The data consists of n independently selected pairs
$(X_i, Y_i), i=1,2,\dots,n$. The variances of X and Y are $\sigma_x^2$ and $\sigma_y^2$, respectively.
Let $D_i = X_i - Y_i$, the $D_i$'s are assumed to be normally distributed with variance $\sigma_D^2$ and the correlation between $X_i$ and $Y_i$ is $\rho$.

a. What is the variance of $\bar{D}$?