1.7 Let X, X be ii.d., each with probability density f,and let Xa) be the smallest...

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1.7 Let X, X be ii.d., each with probability density f,and let Xa) be the smallest of the Xs. Show that Xa is consistent for estimating ξ when (i) f(x)-1 for ξ < x < ξ + 1, f(x) 0 elsewhere; (ii) f(x)-2(x-E) for ξ < x < ξ + 1, f(x)-0 elsewhere: (ii) f(x) for<, f()-0 elsewhere; 120 2. Convergence in Probability and in Law (iv) Suppose that f(x)-0 for all x < ξ. Give a simple condition on f for X(1) to be consistent for estimating ξ which contains (i)-(iii) as special cases. IV Hint: P[X)P(Xi2a)]]

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1.7 Let X, X be ii.d., each with probability density f,and let Xa) be the smallest...

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1.7 Let X, X be ii.d., each with probability density f,and let Xa) be the smallest...

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