A amberxinya Sep 2009 36 0 May 22, 2010 #1 \(\displaystyle \phi_{n}=(1-\frac{x}{T_{n}})^{n-1} , \ \ T_{n}\geq x , \ \ \ 0 \ \ \ otherwise \) \(\displaystyle X_{i} \ \ \ iid \ \ \ E(\lambda) , \ \ \ T_{n}=\sum_{1}^{n}{X_{i}} \) show that, \(\displaystyle E(\phi_{k}|T_{n},\lambda)=\phi_{n} \ \ \ k\leq n\)

\(\displaystyle \phi_{n}=(1-\frac{x}{T_{n}})^{n-1} , \ \ T_{n}\geq x , \ \ \ 0 \ \ \ otherwise \) \(\displaystyle X_{i} \ \ \ iid \ \ \ E(\lambda) , \ \ \ T_{n}=\sum_{1}^{n}{X_{i}} \) show that, \(\displaystyle E(\phi_{k}|T_{n},\lambda)=\phi_{n} \ \ \ k\leq n\)

matheagle MHF Hall of Honor Feb 2009 2,763 1,146 May 22, 2010 #2 you need to know the distribution of \(\displaystyle {X_1\over X_1+\cdots +X_n}\)