Let X and Y be independentrandomvariableswith X Poissonsdis- tributedwithmean and Y exponentiallydistributedwithrate , where >

Let X and Y be independentrandomvariableswith X Poisson’sdis-

tributedwithmean λ and Y exponentiallydistributedwithrate λ, where λ > 0.

a) Representthefamilyofjointdistributionsof (X,Y ) as acurvedexponential familyofdimensiononeandordertwo.

b) Findthelog-likelihoodfunction,scorefunction,Fisherinformation,andquad-

ratic scoreforthefamily.