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