Skip to content
Q57Section C (Section C)57 of 60

UMVUE of theta squared for a Pareto

Let X1,X2,X3,X4X_1,X_2,X_3,X_4 be a random sample from a continuous distribution with probability density function f(x;θ)={2θ2x−3if θ<x<∞, 0otherwise,f(x;\theta)=\begin{cases}2\theta^2 x^{-3}& \text{if }\theta<x<\infty,\ 0& \text{otherwise,}\end{cases} where θ>0\theta>0 is an unknown parameter. It is known that X(1)=min⁡{X1,X2,X3,X4}X_{(1)}=\min\{X_1,X_2,X_3,X_4\} is a complete sufficient statistic for θ\theta. If the observed values are x1=15x_1=15, x2=11x_2=11, x3=10x_3=10, x4=17x_4=17, the uniformly minimum variance unbiased estimate of θ2\theta^2 is equal to __________ (answer in integer)

Numerical answer: type the number (no options).

Type your answer and check it.