# Converges in distribution

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• April 16th 2010, 04:14 AM
anabelle
convergence
If I define $X_1,X_2,...$ as independent RVs, uniformly distributed on [0,1], and I define $M_n=\textup{max}\left \{X_1,...,X_n\right \}$, how would I show that $n(1-M_n)\overset{D}{\rightarrow}X$ as $n\rightarrow \infty$, where $X\sim \textup{Exp}(1)$?

Thanks very much!
• April 22nd 2010, 12:28 AM
Moo
Hello,

Convergence of the cdf's.