Failure distribution function for a given motor is shown below:

$($a$)$ Derive and sketch the failure density function

$($b$)$ Derive and sketch the reliability function

$($c$)$ Derive and sketch the hazard rate function

$($d$)$ What is the probability a new motor will last more than $2$ years?

$($e$)$ Determine the mean time to fail for the motor.

$($f$)$ What is the median time to fail for this motor?