Solved: Suppose that Y1, Y2, . . . , Yn is a random sample
Chapter 9, Problem 45E(choose chapter or problem)
Suppose that \(Y_{1}, Y_{2}, \ldots, Y_{n}\) is a random sample from a probability density function in the (one-parameter) exponential family so that
\(f(y \mid \theta)=\left\{\begin{array}{ll} a(\theta) b(y) e^{-[c(\theta) d(y)]}, & a \leq y \leq b \\ 0, & \text { elsewhere } \end{array}\right.\)
where \(a \text { and } b\) do not depend on \(\theta\). Show that \(\sum_{i=1}^{n} d\left(Y_{i}\right)\) is sufficient for \(\theta\).
Equation Transcription:
{
Text Transcription:
Y1, Y2,...,Yn
f(y \mid \theta)={ a(\theta) b(y) e^-[c(\theta) d(y)], & a \leq y \leq b 0, elsewhere
a and b
\theta
\sum_i=1^n d\left(Y_i \right)
\theta
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