Solve the following:

Let X1, X2, ... be random variables over the same probability space (0, A, P) having the same distribution function F(x). (Nothing else is assumed. ) Let Mn := maxisign |Xil. (a) Suppose that for some a > 0, f laadF(x) 0 and d > 0 lim P(n-(1/at=) | Mn] > 8) = 0. (b) Suppose that for some s > 0, f exp(s|x))dF(x) 0 lim P((bn logn) [Mn| > 8) = 0. Hint: Use the following Markov-like inequality. n P( max Xi > 1 = P( U1 {|Xil> >}) P(IXi > > = nP(|Xil > >). 1