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

Do part c ,d and e

1. Let X1,..., X, be a random sample with each X, having probability density function<br>f(x;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(z) = 1– (6*/z)m,<br>for a2 0º.<br>(c) Hence, or otherwise, determine whether the MLE of 0 is unbiased.<br>(d) Show that method of moments (MOM) estimator of 0 is VE Xi-<br>(e) Calculate the mean squared error of the MLE of 0 when n =<br>= 2.<br>

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Jun 07, 2022

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

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