I had received this homework assignment and I'm not sure how to tackle it.
Let $n\ge1$, $[L, U]$ a confidence interval with a confidence level of $\alpha - 1$, and $\mu$ of minimal length, $D = L - U$ the length of the confidence interval.
Calculate $E(D^2)$
What I'd tried so far is to expand the expression $E(D^2) = E((L - U) ^ 2) = ... = E(L^2) - 2\cdot E(U\cdot L) + E(U^2)$, however I honestly did not know how to proceed.
Can anyone point me in the right direction?
Thank you for your help guys!
I really appreciate it.
- Chen