1. ## Bayesian Estimation

Hi, can you please see the attachment..Thanks!

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. $\displaystyle \Pr(D)$ is the prior probability and $\displaystyle \Pr(D \, | \, A)$ is the posterior probability. Then:

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

$\displaystyle \Pr(A) = (0.95)^3$

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

$\displaystyle \Pr(D)$ is already got.

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