The term 'transition matrix' refers to a matrix that provides a measurement of the probability of a loan: (0.5 marks)Question 15Answera.being upgraded over some period.b.being downgraded over some period.c.defaulting over some period.d.All of the listed options are correct.

In an office complex of 1180 employees, on any given day some are at work and the rest are absent. It is known that if an employee is at work today, there is an 78% chance that she will be at work tomorrow, and if the employee is absent today, there is a 54% chance that she will be absent tomorrow. Suppose that today there are 955 employees at work. (a) Find the transition matrix for this scenario (assume that state 1 is "at work" and state 2 is "absent"). [ ? ? , ? ?] (b) Predict the number that will be at work five days from now. ? (c) Find the steady-state vector. (Note that the sum of the entries must be the total number of employees, but make sure that your answers are correct to at least 1 decimal place.) [? ?]

Quiz Question Consider the Markov chain with transition diagram345210.10.50.50.60.30.50.20.40.30.50.50.20.4i.e., with transition matrixP =0.6 0.4 0 0 00.5 0.5 0 0 00 0.5 0 0.5 00 0.5 0.3 0 0.20 0.1 0.2 0.4 0.3 .(a) Starting from state 5, what is the most likely two-step path? What is the probability(starting from state 5) of following that two-step path?(b) In this Markov chain, can you get from every state to every other state eventually?

Find the transition matrix from B to B'.B = {(4, −1), (3, 2)}, B' = {(1, 0), (0, 1)}STEP 1: Begin by forming the following matrix.[B':B] = STEP 2: Determine the transition matrix.P−1 =

Quiz question For each of the following transition matrices for Markov chains with state spaceS = {1, 2}, write down the Full Balance Equations and find the equilibrium distribution(s).(a) P =0.4 0.60.8 0.2(b) P =0.82 0.180.82 0.18

0 & 0.2 & 0.15 \\0.6 & 0 & 0.25 \\0.5 & 0.1 & 0\end{bmatrix} \]ii) **Determine the probability the professor will purchase the current model in 3 years:**To find the probability of being in the same state after three years (P(Si to Si) for i = 1, 2, 3), we can use matrix exponentiation:\[ P^3 = P \times P \times P \]You can calculate this matrix product using a calculator or software. After obtaining \( P^3 \), look at the main diagonal elements, and each element P(i, i) represents the probability of being in state i after 3 years.So, calculate \( P^3 \) and extract the diagonal elements to find the probability of purchasing the current model in 3 years.