A rat is put into the following maze:2The rat has a probability of 1/4 of starting in any compartment and suppose that therat chooses a passageway at random when it makes a move from one compartmentto another at each time. Let Xn be the compartment occupied by the rat after nmoves.(a) Explain why {Xn} is a MC and find the transition matrix P.(b) Explain why the chain is irreducible, aperiodic and positive recurrent.(c) What is the limit of Pn? Explain.

Given that a rat is put into the maze as

Answered: A rat is put into the following maze: 3…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

We want to train a mouse to follow a particular path in the maze (see image 1). To measure the effectiveness of the training, we want to compare the behaviour of the trained mouse to that of a mouse that runs through the maze at random.(a) Construct the matrix T describing the behaviour of the untrained mouse, where tij gives the probability of going to room i when the mouse is in room j. (Note that since the mouse moves randomly if it is in front of two doors, it has a 1/2 probability of going through each of these doors.) (b) Suppose the mouse begins its journey through the maze with a vector of probabilities P(0) = (see image 3) where pi(0) represents the probability of being in room i at the start; so of course we have p1(0)+p2(0)+p3(0)= 1). Show that the probabilities of being in room i after a change of room P(1) are given by P(1)=TP(0). Indications: proceed with a proof on the one hand and on the other hand: start by calculating the probabilities of being in parts 1,2 or 3 after…
A square matrix [A] is diagonally dominant if (A) la,l2Σa- 1, 2." (B) a, > Ea,i = 1, 2, ...,n and a, >E a, for any i 1, 2, .., n %3D (C) a,> Ea, = 1, 2 ....n and a,|>E, for any i = 1, 2, ..n (D) a,l2 Σa i=1, 2 " = 1, 2, ....n
Please show steps and solutions to solve problem
Please do not give solution in image format thanku
Find an elementary matrix E that corresponds to the row operation of adding – 4 times Row 1 to Row 2. E
Suppose in a scatterplot matrix, you observe that all of the scatterplots associated with the explanatory variables show a strong linear relationship. There are three explanatory variables in the model. Of the following, which is the most valid to do? Remove the response variable. Remove only one of the explanatory variables and keep only two. Remove all of the explanatory variables because they are linearly related to each other and therefore explain the same thing. Remove exactly two of the explanatory variables because they are all linearly related to each other and therefore explain the same thing. We only need to keep one in the model.
4. (a) Prove that if A is an n x n invertible matrix that satisfies the equation A2 = A then A is the identity matrix. (b) Write down a 2 x 2 matrix B that is not the identity but satisfies B² = B. %3D
In at tropical forest, the populations of falcons and mice are related toeach other. The mice eat everything they can while the falcons eat the mice. The population sizes of falcons and mice evolve according to the rule. * At the beginning of 2023, there were 10 falcons and 40 mice. a) Approximately how many falcons and mice will there be at the beginning of 2068? b) c) Find a diagonalization, A = BDB-1, of the transition matrix A from part (b), where D is a 2x2 diagonal matrix, and B is an invertible2x2 matrix. d) Use your answer to (c) to estimate the (approximate) numbersof falcons and mice there will be at the beginning of 2058. e) what restrictions on the initial population sizes ensures the long time survival of both species in the forest
A market demand has 3 possible states namely GOOD, NORMAL and BAD for each period. At each period there are 2 possible decisions for the manager as do nothing/ make promotion. The transition matrix of states regarding for possible decisions are given as below Pof do nothing GOOD NORMAL BAD GOOD 0.4 0.2 04 0.3 0.2 0.5 NORMAL 0.5 BAD 0.1 0.4 Pof make promotion GOOD NORMAL BAD 0.4 0.4 0.5 GOOD 0.2 NORMAL 04 0.1 BAD 0.3 0.4 0.3 It is known that the income for each period when the state in GOOD, NORMAL and BAD are 10000, 7000, 2000. Cost for do nothing is 0, and make promotion is 3000. a) Given at period 0 the state is NORMAL, estimate expected beneft obtain two periods when the sequence of decisions is do nothing, do nothing b) Given at period 0 the state is NORMAL, estimate expected beneft obtain two periods when the sequence of decisions is make promotion, make promotion
M P₁ 0000 P3 Give the adjacency matrix M associated with the directed graph above. P5 ОРА Those longest possible walks all start at the vertex P1 for the vertex P₁, P2 for the vertex P₂, etc. P₂ The smallest integer value n for which M" = 0 (where 0 represents a zero matrix) is This indicates that the longest walk between any two vertices in the graph would have length and end at the vertex (based on the matrix M"-1). Write
Please solve and show soution for question 2

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS