5. (20 points) i. Consider the case when students visit their professor's office at random points in time and find him helping other students. Let X, denote the time (in minutes) that the student has to wait before being admitted to see the professor. 1. Describe the type of the random process Xn, n > 1 along with its space. 2. Sketch one sample path of Xn. li. The random process Y (t) is defined as Y (t) = X + (1 -t), where X is a uniform random variable in the interval [0, 1]. 1. Find the first order probability density function (PDF) of the process Y (t). 2. Is Y (t) a WSS process? Is ergodic? Why? lii. The random process is given by X (t) = Acos(wt) + B sin(wt) where A and B are two independent and identically distributed Gaussian random variables with zero mean and variance o'. Show whether X (t) is a WSS process or not