how to show this

Sep 2009
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\(\displaystyle \phi_{n}=(1-\frac{x}{T_{n}})^{n-1} , \ \ T_{n}\geq x , \ \ \ 0 \ \ \ otherwise \)

\(\displaystyle X_{i} \ \ \ iid \ \ \ E(\lambda) , \ \ \ T_{n}=\sum_{1}^{n}{X_{i}} \)

show that, \(\displaystyle E(\phi_{k}|T_{n},\lambda)=\phi_{n} \ \ \ k\leq n\)
 

matheagle

MHF Hall of Honor
Feb 2009
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you need to know the distribution of

\(\displaystyle {X_1\over X_1+\cdots +X_n}\)