Question: Let X1,..., XN be i.i.d. random variables with a uniform distribution of (0, 0]. Consider the following estimator: (x) = max (X1,...,XN) (a) Show

Let X1,..., XN be i.i.d. random variables with a uniform distribution of

Let X1,..., XN be i.i.d. random variables with a uniform distribution of (0, 0]. Consider the following estimator: (x) = max (X1,...,XN) (a) Show that the PDF of is fa(0) = N[Fx(x)]N- fx (x), where fx and Fx are the PDF and CDF of Xn (b) Show that is a biased estimator. (c) Find a constant c so that c is unbiased.

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