Chapter 7: Problem 5
Let \(X\) be a random variable with pdf of a regular case of the exponential class. Show that \(E[K(X)]=-q^{\prime}(\theta) / p^{\prime}(\theta)\), provided these derivatives exist, by differentiating both members of the equality $$\int_{a}^{b} \exp [p(\theta) K(x)+S(x)+q(\theta)] d x=1$$ with respect to \(\theta\). By a second differentiation, find the variance of \(K(X)\).
Short Answer
Step by step solution
Key Concepts
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