In my documentation they explain me how to calculate specific probabilities of some statistics
like $P(\bar X \ge x)$ or $P(S^2\ge x) $ knowing $X$~$N(\mu,\sigma)$
but then in the exercices they keep asking me things like this:
$P(S^2/\sigma^2 \le 2.041) $ with $ n=16$ and $X$~$(\mu,\sigma)$
or
$P(-1 \le [\bar X- \bar Y-(\mu_X-\mu_Y)]\le1)=95$% knowing: $\sigma^2_X=2$ and $\sigma^2_Y=2.5$ and $k=m=n$ (both are $N(\mu,\sigma)$ (find k)
How can I know the probability of a combination of statistics?( like those two examples) Is there any general rule to calculate a a combination of statistics for each distribution?
Thanks.