Problem 3. Means and Correlations. a. Here we consider mobile phone usage by Alice. Let us model her phone usage as follows: First we pick a random number S uniformly dis- tributed between 0 and 1 minute. This represents the start time of the call. Alice uses the phone for exactly 1 minute each time so ends the first call at time E = S +1. She then makes another call start- ing at a time S2 where S2 is uniformly distributed between E and E+1 and ends the call at time E2 = S2 +1. This process contin- ues until Alice has made and completed N calls with Alice starting a call at a time Sk where S is uniformly distributed between Ek-1 and Ek-1+1 and ends the call at time Ek = Sk +1, k = 1, 2,..., N, with Eo = 0. Let us define X(u, t) = 0 when Alice is not using the phone and X(u,t) = 1 when Alice is using the phone, where u is a realization from an N-dimensional sample space, i.e., u = = {U1, U2,..., UN}, with each u,, i = 1, 2, ..., N, uniformly distributed in (E-1, E-1+1). Then X(u, t) is a random process. Below is an example of a sample function for N = 3. 1 0 S E S2 E2 S3 E3 i. Compute E[X (u, t)] for 0 < t