Let $\{x_n\}_{n=1}^{+\infty}$ independent identically distributed uniformly on $[a,b]$ random variables, $f_n=\max\{x_1, x_2,..x_n\}$, $g_n=\min\{x_1, x_2,..x_n\}$. Prove that for $n\frac{b-f_n}{b-a}$ weakly converges to exponential distribution with parameter $1$.
Weakly converges to exponential distribution with parameter 1
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probability
convergence
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1see if you can show it for the interval $[0,1]$ first. Also what's the use of defining $g_n$? – 2012-10-16