Management Science subject

1. Given the initial state vector (1,0) and the transition matrix shown below, find the state vector corresponding to two steps later (n = 2). a. (0.2002, 0.7998) b. (0.8086, 0.7998) (0.8086, 0.1914) 0.13 0.87 [0.7998, 0.2002) 0.91 0.09 Choose the correct transition matrix representing the Morkov chain with state dia gram shown below. Assume the states are ordered with A before B. a. (0.13 0.87) 0.91 0.09 0.13. 0.87 b. (0.13 0.91) 0.87 0.09 0.09 A B C. (0.13 0.87) 0.09 0.91 0.91 d. (0.87 0.09 0.13 0.91) 3. A certain stock price has been observed to follow a pattern. If the stock price goes up one day, There's a 20% chance of it rising tomorrow, a 30 chance of it falling, and a 50% chance of it remaining the same. If the stock price falls one day, Ibere's o 35%% chance of it rising tomorrow, a 50% chance of it falling, and a 15% chance of it remaining the some. Finally, if the price is stable on one day, then it has a 50-50 change of rising or folling the next day. Which matrix below is the transition matrix for this Markov chain, if we list states in the order: [rising, falling, constant]. 20 30 35 50 15 SO 1012 0.35 05 03 0.5 0.5 05 0.15 0 35 50 C 30 50 50 50 15 102 03 05 d. 035 05 0.15 105 105