Markov process The final exam in Humanities 10 always includes either a question about the Iliad or a question about the Odyssey. The choice is made by rolling a die, according to the following rules: - If the exam in year n had an Iliad question, the exam in year n+1 will have an Iliad question if the die roll is even, an Odyssey question if the die roll is odd. - If the exam in year n had an Odyssey question, the exam in year n+1 will have an Odyssey question if the die roll is 1, an Iliad question otherwise. (a) Write a 2x2 transition matrix in which element a
i,j
represents the probability of transitioning from state j to state i (b) You know that there was an Iliad question in 2021. Use matrix multiplication to calculate the probability of an Iliad question in 2024. (c) You are planning that your first child will take Humanities 10 some time in the 2040s. Estimate the probability that there will be an Iliad question on the final exam. (Hint: find a vector of probabilities that does not change from year n to year n+1.)