Question $6$

$1\mathrm{.}25pts$

An acid solution made by mixing a powder compound with water is used to etch aluminum. The $pH$ of the solution, $x,$ will vary due to slight variations in the amount of water used, the potency of the dry compound, and the $pH$ of the water itself. Assume that $x$ is gamma distributed with $$ and $$ unknown. Using the method of moments, find the point estimate, hat$(),$ for the unknown parameter $$ using the data below.

$\backslash$table$[[1\mathrm{.}2.,2\mathrm{.}0.,1\mathrm{.}6,1\mathrm{.}8,1\mathrm{.}1],[2\mathrm{.}5,2\mathrm{.}1,2\mathrm{.}6,2\mathrm{.}2,1\mathrm{.}7],[1\mathrm{.}5,1\mathrm{.}7,2\mathrm{.}0,3\mathrm{.}0,1\mathrm{.}8]]$

Adapted from Milton & Arnold, $4$th edition, page $249.$

$0\mathrm{.}0667$

$15\mathrm{.}0098$

$7\mathrm{.}8176$

$0\mathrm{.}1279$

Question $7$

$1\mathrm{.}25pts$

Given the problem situation in Question $6,$ use the method of moments to find the point estimate, hat$(),$ for the unknown parameter, $.$

$2\mathrm{.}0479$

$0\mathrm{.}1279$

$-26\mathrm{.}7521$

$0\mathrm{.}2456$