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Math Help - Bayes Estimator

  1. #1
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    Bayes Estimator

    The breaking strength of a type of cloth is to be measured for 20 specimen. The underlying distribution is normal with unknown mean \theta but with a standard deviation of 3. Suppose that the unknown mean has a prior distribution that is normal with mean 200 and standard deviation 2. If the average breaking strength for this sample of 20 specimen is 182, determine the Bayes estimate of \theta and an interval around this value that contains \theta with probability .95.

    Is this correct?

    E(\theta|data) = \frac{1/4}{1/9+1/4}(200) + \frac{1/9}{1/9+1/4}(182) = 194.46

    Var(\theta|data) = \frac{1}{1/9+1/4} = 36/13

    P\{-1.96<\frac{\theta-194.46}{\sqrt{36/13}}<1.96|data\} = .95

    \theta \in (191.20, 197.72) \mbox{ with .95 probability}

    How do I determine the Bayes estimate of \theta?
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  2. #2
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    Can anyone verify this please?
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