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Let X1,..., Xn be a random sample from a distribution with pdf as follows: fX(x) =...

Let X1,..., Xn be a random sample from a distribution with pdf as follows:

fX(x) = e^-(x-θ) , x > θ

0 otherwise.

Find the sufficient statistic for θ.

Find the maximum likelihood estimator of θ.

Find the MVUE of θ,θˆ

Is θˆ a consistent estimator of θ?

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