Exercise1.3 Which ofthedistributionsinExercise1.2belongtotheexponentialfamily?Findtheir natural parameters.Inaddition,consideralsothefollowingdistributions: 1. Poisson distribution Pois() 2. Cauchydistribution f (y) = 1 (1+(y)2) ,

Exercise1.3 Which ofthedistributionsinExercise1.2belongtotheexponentialfamily?Findtheir natural parameters.Inaddition,consideralsothefollowingdistributions:

1. Poisson distribution Pois(λ)

2. Cauchydistribution fθ (y) = 1

π(1+(y−θ)2) , −∞ < y < ∞

3. fθ (y) = θ

(1+y)θ+1 , y ≥ 0, θ > 0 4. fθ (y) = θyθ−1, 0 < y < 1, θ > 0 5. fθ (y) = 2(y+θ)

1+2θ , 0 < y < 1, θ > 0