Thread: Finding minimum variance unbiased estimator (MVUE)

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

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.