The largest order statistic, i.e., the max is sufficient for theta.
Next, as you are asked to do, obtain the density of this order stat.
Use nf(x)[F(x)}^(n-1)
Then otain the expected value of the max and compare that to theta.
Random sample Y1,....,Yn with pdf:
f(y|θ) = 3y^2/θ^3, 0<y<θ and 0 elsewhere
Given Y(n) = max(Y1,...,Yn) is sufficient for θ,
a) Show that Y(n) has pdf:
f(n)(y|θ) = 3ny^(3n-1)/θ^(3n) , 0<y<θ and 0 elsewhere
b) Find MVUE for θ
I am unsure as to how to start these so any help is appreciated