4. A frog is randomly jumping on the vertices of a cube. At each time period, the frog stays at its current vertex with probability 1/4. With probability each of 1/4, the frog chooses one of the three edges and jumps to an adjacent vertex. The frog starts from vertex v at time 0. N INDENG 263A Assignment #1 a.) Construct a Markov chain that models the dynamics of the frog. b.) Compute the expectation of the first time (denoted by 7) the frog jumps to the antipodal vertex w. (Two points are antipodal (i.e., each is the antipode of the other) if they are diametrically opposite.) c.) Use first transition analysis to derive a linear system of equations for ET2. d.) Use first transition analysis to derive a linear system of equations to compute the probability that once the frog leaves v, the frog returns to v before ever reaching w