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May 23, 2019
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(Solved) : Use R Show Code Problem 2 Inspector Receives Batch Widgets Used Manufacture New Product Ba Q28095270 . . .

Use R and SHOW ALL CODE

## Problem 2
*An inspector receives a batch of widgets which will be used tomanufacture a new product. The batch will be rejected and sent backto the manufacturer if the proportion of defective widgets in thebatch exceeds 10%. The inspector selected thirty widgets from thebatch and tested them. He found that of the thirty widgets hetested, two were defective.*

*Let the proportion of defective widgets in the batch, $p in{0.1, 0.2, 0.3, …, 0.9}$, and assign a uniform prior to $p$(that is, according to the prior distribution, $P(p = p_i) = P(p =p_j)$ for every $p_i, p_j in {0.1, 0.2, 0.3, …, 0.9}$; inwords, each $p$ is equally likely). Given the results of theinspection:*

*Compute the maximum* a-posteriori *(MAP) estimator for $p$ anda (approximately) 95% credible interval for $p$ using the posteriordistribution.*

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