Coefficients Intervals


TS Contributor
Hello people,

I need ideas about this question:

let x1,x2,...,xn be a random sample: x1,x2,...,xn ~ N(myu, sigma^2)
( myu is known )
and let y1,...ym be another random sample: y1,y2,...ym ~ exp ( lamda )

find a coefficients interval for lamda*sigma^2

I know that a pivotal for sigma^2 is distributed chi squared and so is a pivotal for lamda ( because a sum of Xi's from the exp distribution is distributed erlang and 2*lamda*sum(Xi) is distributed chi squared )

I also know that chi squared / chi squared is F, but what is chi squared*chi squared ?

( sorry about my english ! )
thanks !