Exercise7.6 There isadeviceforbloodtypeclassification:A,B,ABorO.Itmeasuresacertain quantity Y, whichhasashiftedexponentialdistributionwiththedensity f (Y)=e(y), y, 0. If0 < 1,

Exercise7.6 There isadeviceforbloodtypeclassification:A,B,ABorO.Itmeasuresacertain quantity Y, whichhasashiftedexponentialdistributionwiththedensity fτ (Y)=e−(y−τ), y≥τ, τ ≥

0. If0 ≤ τ < 1, thebloodisoftypeAB;if1 ≤ τ < 2, thebloodisoftypeA;if2 ≤ τ < 3, theblood is oftypeB;andif τ ≥ 3, thebloodisoftypeO.Itisknownthatinthepopulationasawhole,

τ ∼ exp(1).

The lossofmisclassifyingthebloodisgiveninthefollowingtable:

Classified As AB ABO True AB 0 112 Blood A 1 022 Type B 1 202 O 3 330 A patienthasbeentestedand y = 4 isobserved.WhatistheBayesaction?