Let X1,..., XN be i.i.d. uniform random variables distributed over (0, 1]. Suppose Y1,...,YN are defined...

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Let X1,..., XN be i.i.d. uniform random variables distributed over (0, 1]. Suppose Y1,...,YN are defined as follows. Show that Yn converges in probability to some limit (please identify the limit): (a) Yn = (Xn)" %3D (b) Yn = max (X1,..., Xn) Let X1,..., XN be i.i.d. uniform random variables distributed over (0, 1]. Suppose Y1,...,YN are defined as follows. Show that Yn converges in probability to some limit (please identify the limit): (a) Yn = (Xn)" %3D (b) Yn = max (X1,..., Xn)