Worked Example 2
Given that the random variables $X$ and $Y$ have distributions $N(60, 25)$ and $N(54, 64)$ respectively, and that $\bar{X}$ and $\bar{Y}$ denotes the means of $7$ independent observations of $X$ and $11$ independent observations of $Y$ respectively.
State the sampling distributions of
(i)
$\bar{X}-\bar{Y}$
(ii)
$2\bar{X}+5\bar{Y}$
(iii)
$\frac{{{X}{1}}+{{X}{2}}+{{X}{3}}-{{Y}{1}}-{{Y}{2}}-…-{{Y}{5}}}{8}$
