Let Mn be the maximum of n independent U(0, 1) random variables. a. Derive the exact expression for P(|Mn − 1| > ε) b. Show that limn→∞ P(|Mn − 1| > ε) = 0. Can this be derived from Chebyshev’s...

Let Mn be the maximum of n independent U(0, 1) random variables.

a. Derive the exact expression for P(|Mn − 1| > ε)

b. Show that limn→∞ P(|Mn − 1| > ε) = 0. Can this be derived from Chebyshev’s inequality or the law of large numbers?