A recruiter at a company is attending a university$$s career fair. He has decided to

send an email asking for newer employees to volunteer and talk about their job experience and work$-$life balance at the company with students attending the career fair. The recruiter sends the email to $15$ newer employees. Suppose that the time it takes each of the employees to respond is an independent exponential random variable with a mean $45$ minutes. The recruiter will stop checking emails after he gets $5$ responses, and he constantly monitors his email until he gets those $5$ responses. If T is the amount of time the recruiter is monitoring his emails,

$($a$)(10$ points$)$ Find E$[$T $].$

$($b$)(10$ points$)$ Find Var$($T $)$