Let Y1, Y2, . . . , Yn denote a random sample of size n

Chapter 8, Problem 11E

(choose chapter or problem)

Let \(\mathrm{Y}_{1}, \mathrm{Y}_{2}, \ldots, \mathrm{Y}_{\mathrm{n}}\) denote a random sample of size n from a population with mean 3. Assume

that \(\widehat{\theta}_{2}\) is an unbiased estimator of \(E\left(Y^{2}\right)\) and that \(\widehat{\theta}_{3}\) is an unbiased estimator of \(E\left(Y^{3}\right)\). Give

an unbiased estimator for the third central moment of the underlying distribution.

Equation Transcription:

 

 

Text Transcription:

Y1, Y2,...,Yn

\widehat\theta_2

E\left(Y^2\right)

\widehat\theta_3

E\left(Y^3\right)

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