Data is generated from the exponential distribution with density $f(y)=$

$exp(-y)$ where $,y>0.$

$($a$)$ Identify the specific form of $,,a(),b()$ and $c()$ for the exponential distribu$-$

tion.

$($b$)$ What is the canonical link and variance function for a GLM with a response

following the exponential distribution?

$($c$)$ Identify a practical difficulty that may arise when using the canonical link in

this instance.

$($d$)$ When comparing nested models in this case, should an $F$ or ${}^2$ test be used?

Explain.

$($e$)$ Express the deviance in this case in terms of the responses $y_i$ and the fitted

values hat$({)}_i.$