Let X1, X2, X3, ..., Xn be independently and identically distributed random variables with f(x,theta)=3x^2/theta^3; 0<x<theta; 0 otherwise. The UMVUE of theta^r is given by

Q33Section I (Objective (Q1–Q80))33 of 80

Statistical Inference — UMVUE of theta to the r for a power-function density

Let $X_1, X_2, X_3, ..., X_n$ be independently and identically distributed random variables with $f(x,\theta)=\frac{3x^2}{\theta^3}$ ; $0<x<\theta$ ; $0$ otherwise. The UMVUE of $\theta^r$ is given by

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