1. Sea \( p(x \mid \theta) \) el modelo paramétrico exponencial con parámetro desconocido \( \theta \) y supongamos que la información a priori sobre \( \theta \) está dada por \( p(\theta)=\operatorname{gamma}(\theta \mid a, b) \). a) Suponiendo observaciones muestrales independientes, obtenga la distribución a posteriori de \( \theta \). b) Da el estimador de Bayes para \( \theta \).
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Step 1: **Identify the likelihood function based on the given model** Given that \( p(x \mid \theta) \) is an exponential model, the probability density function (PDF) for the exponential distribution is: \[ p(x \mid \theta) = \theta e^{-\theta x} \] for \( x \geq Show more…
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