Mathematics · Bayes Estimation
Suppose the conditional probability density function of a random variable X given θ is f(x|θ) = 2xθ2 for 0 < x < θ, and 0 otherwise. Let the prior distribution of θ be Uniform(0, 1). Based on a single observation x from X, the Bayes estimate for θ under the squared error loss function is:
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 12x1 + x
- 2x
- 3- x loge x1 - x
- 4-x loge x✓
Correct answer
-x loge x
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