Chapter 8.2, Problem 11E

Let Y₁, Y₂, … , Y_n denote a random sample of size n from a population with mean 3. Assume that ${\hat{\theta }}_2$ is an unbiased estimator of E(Y²) and that ${\hat{\theta }}_3$ is an unbiased estimator of E(Y³). Give an unbiased estimator for the third central moment of the underlying distribution.