Let Y 1 , Y 2 , , Y n be a random sample from f Y (y ) 1 e y , y 0 Compare the Cramr Rao lower bound for f Y (y ) to the variance of the maximum likelihood estimator for , 1 Is Y a best estimator for

Question: Let Y 1 , Y 2 , . . . , Y n be a random sample from f Y (y; ) = 1/ e

Let Y₁, Y₂, . . . , Y_n be a random sample from f_Y(y; θ) = 1/θ e^−y/θ, y > 0. Compare the Cramér-Rao lower bound for f_Y(y; θ) to the variance of the maximum likelihood estimator for θ, ˆθ = 1 . Is Y̅ a best estimator for θ?

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