Let$12,,,$ nY Y Y denote a random sample from the density function given by$11$ exp $,0,0$

$(|)$

$0,$ elsewhere

r

r y

ry y

f y

$$

$$

$$

$$

$$

$=$

$$

$$

$.$

where r is a known positive constant.

$($a$)$ What is the Likelihood Function for this distribution?

$($b$)$ Use the Factorization Theorem to determine a sufficient statistic for the parameter$.$

$($c$)$ What is the Log$-$Likelihood Function for this distribution? Simplify where possible.

$($d$)$ Use the Method of Maximum Likelihood to determine the MLE of$.$