For n independentobservations {yi} from thegamma pdf (2.10), withshapeparameter k known (suchaswiththeexponentialdistributionspecialcase): (a) FindthelikelihoodfunctionandshowthattheMLestimatorof is

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For n independentobservations {yi} from thegamma pdf (2.10), withshapeparameter k known

(suchaswiththeexponentialdistributionspecialcase):

(a) FindthelikelihoodfunctionandshowthattheMLestimatorof λ is ˆλ = k~Y .

(b) WhatistheMLestimator of E(Y ) = k~λ?

(c) Showthatthelarge-samplevarianceof ˆλ is λ2~kn.

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