Chapter 17.6, Problem 12P

This study presents the one-step transition probabilities for a renewal Markov chain exhibiting zero recurrence.

The following is an illustration of the one-step transition probabilities for a renewal Markov chain with no recurrence.

I can't figure out this question. Does anyone know how to solve it? Q: Give an example of one-step transition probabilities for a renewal Markov chain that is null recurrent.

Example one-step transition probabilities for a renewal Markov chain with zero recurrence.

Consider the case of a simple Markov Decision Process (MDP) with a discount factor gamma = 1. The MDP has three states (x, y, and z), with rewards -1, -2, 0, respectively. State z is considered a terminal state. In states and y there are two possible actions: a₁ and a2.   The transition model is as follows:   In state x, action a1 moves the agent to state y with probability 0.9 and makes the agent stay put with probability 0.1. In state y, action a1 moves the agent to state with probability 0.9 and makes the agent stay put with probability 0.1. In either state or state y, action a2 moves the agent to state z with probability 0.1 and makes the agent stay put with probability 0.9. Please answer the following questions:                                       Draw a picture of the MDP  What can be determined qualitatively about the optimal policy in states x and y? Apply the policy iteration algorithm discuss in class, showing each step in full, to determine the optimal policy and the…

Consider the illustration: Suppose that a group of robots is traversing this maze. At each step, each robot will choose a path and move along it, where it is equally likely to select each available path and cannot choose to stay where it is. (At the end of each step, each robot will be in one of the four numbered rooms.)     Part (a): Construct the appropriate transition matrix for the Markov chain modeling this scenario.     Part (b): Find the steady state probability vector.

i. Draw an MDP with one start state, one end state, and at least 2 intermediary states.ii. Set valid transition probabilities and any rewards for each transition in the MDP above.iii. Run 2 iterations of the value iteration on the MDP above

Specifically, it would be helpful to see an illustration of transition probabilities for a zero-recurrence renewal Markov chain.

In the Erdös-Rényi random network model, suppose N=101 and p=1/20, that is, there are 101 vertices, and every pair of vertices has a probability of 1/20 of being connected by an edge. For the network model given what is the probability that a network generated with those parameters has exactly 400 edges? No need to give the decimal value, the mathematical expression will suffice