Let X and Y be independentandexponentiallydistributedwith E(X) = og E(Y ) =3. Considerthefollowingtwoestimatorsof : is thegammafunction.

Let X and Y be independentandexponentiallydistributedwith E(X) = λ og E(Y ) =3λ. Considerthefollowingtwoestimatorsof λ: 

is thegammafunction.

a) Whichoftheseestimatorsareunbiasedestimatorsof λ?

b) Determinethevarianceforbothoftheseestimators;

c) ComparethevariancestotheCramér–Raolowerboundandcommentontheres-
ult;

d) Whichoftheestimatorshasthesmallestmeansquareerror?

e) Confirmthefindingsaboveviaasimulationexperiment.

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=(3x+Y)/6, X = XY/3. In the following you may without proof use that I(1.5) = F(0.5)/2 = /2, where F(y) = |u u-e" du