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Math Help - Bayesian Estimation

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    Bayesian Estimation

    Hi, can you please see the attachment..Thanks!
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    Quote Originally Posted by aadbaluyot View Post
    Hi, can you please see the attachment..Thanks!
    Please stop attaching word documents and start typing the questions out.

    I assume you know how to get the prior probability (the sample of 50 is assumed to come from a large population so that the Binomial distribution can be used etc.).

    For convenience, let A be the event 3 items in the sample are non-defective. \Pr(D) is the prior probability and \Pr(D \, | \, A) is the posterior probability. Then:

    \Pr(D \, | \, A) = \frac{\Pr(D \cap A)}{\Pr(A)} = \frac{\Pr(A \, | \, D) \cdot \Pr(D)}{\Pr(A)}


    \Pr(A) = (0.95)^3

    \Pr(A \, | \, D) = \frac{{50 - D \choose 3} \cdot {D \choose 0}}{{50 \choose 3}} = \frac{{50 - D \choose 3}}{{50 \choose 3}}

    \Pr(D) is already got.

    Now substitute \Pr(D),  \Pr(A \, | \, D) and \Pr(A) into \frac{\Pr(A \, | \, D) \cdot \Pr(D)}{\Pr(A)} and simplify.
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