1. Let X1,..., X, be a random sample with each X, having probability density function f(r;0) = 36°x¬*, 0


1. Let X1,..., X, be a random sample with each X, having probability density function<br>f(r;0) = 36°x¬*, 0< o² <x< oo.<br>(a) Find the maximum likelihood estimator (MLE) of 0.<br>(b) Show that the distribution function F of min,<ign X, is<br>F(x) = 1 – (6* /z)m,<br>for a2 0º.<br>(c) Hence, or otherwise, determine whether the MLE of 0 is unbiased.<br>

Extracted text: 1. Let X1,..., X, be a random sample with each X, having probability density function f(r;0) = 36°x¬*, 0< o²=""><>< oo.="" (a)="" find="" the="" maximum="" likelihood="" estimator="" (mle)="" of="" 0.="" (b)="" show="" that="" the="" distribution="" function="" f="" of="">

Jun 07, 2022
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