3. 10 p1: A cloud computing facility performs batch processing on job requests that come over night. Each job takes a random amount of time T to complete, independently of other jobs. The PMF of T is given by 2-t t= 1,2,... pr\") = { 0 otherwise where T represents time in minutes. The number of jobs, which we denote N , received over night is also random. In particular, the PMF of N is given by 10\" _10 \"KmWe , n0,1,... (a) 1 pt What type of random variable is T, and what are its mean and variance? (b) 1 pt What type of random variable is N , and what are its mean and variance? (c) 4 pt Compute the expected time for the completion of all the jobs that arrive at the facility over night. (d) 4 pt Compute the conditional expected time for the completion of all the jobs that arrive at the facility over night given that at most 2 jobs have arrived