Suppose a process begins at one state and progresses to another state after 3 turns. Which pair start, end is most likely?
A Markov chain has transition matrix
What is its -step transition matrix?
(A):
(B):
(C):
(D):
Phineas is flipping a fair coin repeatedly and marking down the results. However, he has a soft spot for heads, so half the time he marks heads, he marks heads again. (This means he could possibly mark down heads many times in a row without actually flipping the coin again.) The resulting sequence of states could be modeled by a Markov chain, where the first possible state (and row of the matrix) is heads and the second possible state is tails. What is its transition matrix?
(A):
(B):
(C):
(D):
A Markov chain can be constructed for the weather based on the following table.
States | Rainy Tomorrow | Cloudy Tomorrow | Sunny Tomorrow |
Rainy Today | |||
Cloudy Today | |||
Sunny Today |
If it is rainy today, what is the probability that it will be rainy in three days?
If a Markov chain has transition matrix and states and , then what is the value of ?