1. 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, there's a 35% chance of it rising tomorrow, a 50% chance of it falling, and a 15% chance of it remaining the same. Finally, if the price is stable on one day, then it has a 50-50 change of rising or falling 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 50 35 50 15 50 50 0 0.2 0.35 0.5 0.3 0.5 0.5 0.5 0.15 20 35 50 30 50 50 50 15 0 0.2 0.3 0.5 0.35 0.5 0.15 0.5 0.5 2. Choose the correct transition matrix representing the Markov chain with state diagram shown below. Assume the states are ordered with A before B. 0.13 0.87 0.09 A B 0.91 0.13 0.87 0.91 0.09 0.13 0.91 0.87 0.09 0.13 0.87 0.09 0.91 0.87 0.09 0.13 0.91 3. Given the initial state vector (1, 0) and the transition matrix shown below, find the state vector corresponding to two steps later (n = 2). ( 0.13 0.87 0.91 0.09 O (0.2002, 0.7998) O (0.8086, 0.7998) O (0.8086, 0.1914) O (0.7998, 0.2002)

1. 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, there's a 35% chance of it rising tomorrow, a 50% chance of it falling, and a 15% chance of it remaining the same. Finally, if the price is stable on one day, then it has a 50-50 change of rising or falling 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 50 35 50 15 50 50 0 0.2 0.35 0.5 0.3 0.5 0.5 0.5 0.15 20 35 50 30 50 50 50 15 0 0.2 0.3 0.5 0.35 0.5 0.15 0.5 0.5 2. Choose the correct transition matrix representing the Markov chain with state diagram shown below. Assume the states are ordered with A before B. 0.13 0.87 0.09 A B 0.91 0.13 0.87 0.91 0.09 0.13 0.91 0.87 0.09 0.13 0.87 0.09 0.91 0.87 0.09 0.13 0.91 3. Given the initial state vector (1, 0) and the transition matrix shown below, find the state vector corresponding to two steps later (n = 2). ( 0.13 0.87 0.91 0.09 O (0.2002, 0.7998) O (0.8086, 0.7998) O (0.8086, 0.1914) O (0.7998, 0.2002)

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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