#transition-matrix

Question 1: Select all that apply

mediumAI-checkedProbabilistic & Graphical Models

A Markov chain has states $s_1, \dots, s_n$ , an initial distribution $\pi_0$ (a row vector) and a transition matrix $T$ whose entry $a_{ij}$ is the probability of moving from $s_i$ to $s_j$ . Which statements are true? Select all that apply.

Under the Markov assumption, the state at time $t+1$ is independent of the states before time $t$ even when the state at time $t$ is unknown1
The probabilities of moving from a given state to every state, itself included, sum to 12
The self-loop probabilities of all the states sum to 13
The distribution over states at time step $k$ is $\pi_0 T^k$ 4

Timed test