Consider n independentobservationsfromanexponential pdf f(y ) ey for y 0, with parameter 0 for which E(Y ) 1 (a) Findthesufficient statisticforestimating (b) Findthemaximumlikelihoodestimatorof and of E(Y ) (c) Onecanshowthat 2(i Yi) has achi squareddistributionwith df 2n Explainwhy 2(i Yi) is apiv...

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Consider n independentobservationsfromanexponential pdf f(y; ) = ey for y 0, with parameter > 0

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Consider n independentobservationsfromanexponential pdf f(y; λ) = λe−λy for y ≥ 0, with parameter λ > 0 for which E(Y ) = 1~λ.

(a) Findthesufficient statisticforestimating λ.

(b) Findthemaximumlikelihoodestimatorof λ and of E(Y ).

(c) Onecanshowthat 2λ(Σi Yi) has achi-squareddistributionwith df = 2n. Explainwhy 2λ(Σi Yi) is apivotalquantity,anduseittoderivea95%confidenceintervalfor λ.

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Foundations Of Statistics For Data Scientists With R And Python

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Authors: Alan Agresti

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Consider n independentobservationsfromanexponential pdf f(y; ) = ey for y 0, with parameter > 0

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Foundations Of Statistics For Data Scientists With R And Python

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