Exercise4.14 Let Y1, ...,Yn be arandomsamplefromadistributionwiththedensityfunction f (y) = y1, 0 y 1, >

Exercise4.14 Let Y1, ...,Yn be arandomsamplefromadistributionwiththedensityfunction fθ (y) = θyθ−1, 0 ≤ y ≤ 1, θ > 0.

1. Showthattheuniformdistribution U (0,1) is aparticularcaseof fθ (y).

2. Find theGLRTatlevel α for testingthehypothesisthatthedatacomesfrom U (0,1).

(Hint: showthat −lnYi ∼ exp(θ).)