Consider the two state switch model from the videos with state space S = {1,2} and transition rate matrix [-A A - where A=1 and µ = 1.5. (a) If the system is in state 1, what is the mean time until it transitions to state 2? Number (b) Evaluate P11 (0) Number (c) Evaluate P11 (0.4) Number (d) Evaluate P21 (0.4) Number

Then, what does the equation, d/dt Π = MΠ means? (where M is a 4x4 transition rate matrix)

Find the transition matrix from B to B'. B = {(1,0) , (0, 1)}, B' = {(1,1), (5, 6)} -5 [1 5 5 6 6

5. Suppose that the results of a peak-hour trip generation analysis for a five-zone small urban area is as follows: Trip Productions: Pi=11,000 P:-93,300 Ps=12,900 P-203,500 Ps-90,700 person-trips Trip Attractions: A,=135,800 Az=57,500 A,-80,900 A,-72,000 Aş=85,200 person-trips Given the following friction factor matrix (based on travel time and cost factors) as follows: Fy Matrix To zone ilj 2 3 4 5 1 From Zone 2 0.78 0.44 0.55 0.28 0.28 0.44 1.30 0.40 0.70 0.33 3 0.55 0.40 1.30 0.44 0.80 4 0.28 0.70 0.44 1.80 0.44 5 0.28 0.33 0.80 0.44 1.80 Calculate the expected peak-hour trip distribution from zone 2 to zone 5 (T25 =?).