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let-x-be-uniformly-distributed-on-0-theta-where-theta-in-0-infty-is-an-unknown-parameter-gi-pa853

Let

`x`

be uniformly distributed on

`0,\theta `

, where

`\theta in(0,\infty )`

is an unknown parameter.Given an i.i.d. sample

`x_(1),dots,x_(n)`

, construct two unbiased estimator based on (i)

`\sum_i^n x_(i)`

and (ii)

`max_(i)x_(i)`

. Which one is a better estimator? Justify your answer.