Let Y1, Y2, . . . , Yn denote independent and
Chapter 9, Problem 78E(choose chapter or problem)
Let \(Y_{1}, Y_{2}, \ldots, Y_{n}\) denote independent and identically distributed random variables from a power family distribution with parameters \(\alpha \text { and } \theta=3\). Then, as in Exercise , if \(\alpha>0\),
\(f(y \mid \alpha)=\left\{\begin{array}{ll} \alpha y^{a-1 / 3^{a}}, & 0 \leq y \leq 3 \\ 0, & \text { elsewhere }
\end{array}\right.\)
Show that \(E\left(Y_{1}\right)=3 \alpha /(\alpha+1)\) and derive the method-of-moments estimator for \(\alpha\).
Equation Transcription:
{
Text Transcription:
Y1, Y2,...,Yn
\alpha and \theta=3
\alpha>0
f(y| \alpha)={\alpha y^0-1 / 3^\alpha, & 0 \leq y \leq 3 0, elsewhere
E\left(Y_1\right)=3 \alpha /(\alpha+1)
\alpha
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