Hello! I have the following matrix (picture 1.)and I am susposed to find the transition matrix ($$ \phi $$) now for that I need the eigenvalue and vectors of this matrix A. The eigenvalues are 1,1 and 2. The eigenvectors I have found to be (1 0 0) (1 1 0) (5 3 1). Now to find the transition...
b)Suppose that the coin flipped on Monday comes up heads. What is the probability that the coin flipped on Friday of the same week also comes up heads?
My attempt to answer this question:
Summary: Finding the transition matrix of a paint ball game where only 3 probabilities are given.
We have the following question:
Alice, Tom, and Chloe are competing in paint ball. Alice hits her target 40% of the time, Tom hits his target 25% of the time, and Chloe hits her target 30% of the...
Consider a Markov chain with state space {1, 2, 3, 4} and transition matrix P given below:
Now, I have already figured out the solutions for parts a,b and c. However, I don't know how to go about solving part d? I mean the question says we can't use higher powers of matrices to justify our...
In a 2012 article published in the Mathematical Gazette, in the game of golf hole score probability distributions were derived for a par three, four and five based on Hardy's ideas of how an hole score comes about. Hardy (1945) assumed that there are three types of strokes: a good (##G##)...
The note I get from the teacher states that for transition matrix, the column part will be current state and the row part will be future state (let this be matrix A) so the sum of each column must be equal to 1. But I read from another source, the row part is the current state and the column...
I want to calculate transition amplitudes in QCD for processes like ##q(k)q^\prime(p)\rightarrow q(k^\prime)q^\prime(p^\prime)##, where ##q,q^\prime## are quarks. However, I am unsure what to do with the colour indices of the quark spinors upon squaring the matrix element. For the sake of...
I just discovered this website and want to thank everyone who is willing to contribute some of their time to help me. I appreciate it more than you know
First off, assume that state 1 is Chinese and that state 2 is Greek, and state 3 is Italian.
A student never eats the same kind of food for 2...
Hey! :o
An octopus is trained to chosose from two objects A and B always the object A. Repeated training shows the octopus both objects, if the octopus chooses object A, he will be rewarded. The octopus can be in 3 levels of training:
Level 1: He can not remember which object was rewarded...
Homework Statement
Find the transition matrix ##P## of a transformation defined as
##T:ℝ_2→ℝ_3##
##T:\begin{bmatrix}a\\b\end{bmatrix} = \begin{bmatrix}a+2b\\-a\\b\end{bmatrix}##
For basis
##B=\begin{bmatrix}1\\2\end{bmatrix},\begin{bmatrix}3\\-1\end{bmatrix}##...
Hello everybody.
I have a Markowian homogeneous random walk. Given the transition matrix of the chain, I know that
##P[ X(t) = i | X(t-1) = j ] ≡ P_{j→i}=T_{ij}##
where ##T## is the transition matrix and ##X(t)## is the position of the walker...
Homework Statement
Define a simple random walk Yn on a finite state space S = {0, 1, 2, . . . , N} to be a random process that
• increases by 1, when possible, with probability p,
• decreases by 1, when possible, with probability 1 − p, and
• remains unchanged otherwise.
(a) Specify the...
Homework Statement
[/B]
The population is 50
The diseases is known to follow SIS dynamics with the following probabilities
The number of infected individuals increases with probability 0.1
and it decreases with probability 0.05
the probability that nothing happens is 0.85
a) what is the...
Hi! I have a question regarding making the transition matrix for the corresponding probabilities. The main problem I feel I have here is figuring out how to represent the probabilities in the question in the transition matrix. Like if something is 7 times more likely than something else.. Any...
Homework Statement
Consider a quantum mechanical system with three states. At each step a particular particle transitions from one state to a different state.
Empirical data show that if the particle is in State 1, then it is 7 times more likely to go to State 2 at the next step than to State...
Hi, guys.
A type of problem that often appears is to find the relation between cross sections of some processes. An example would be:
$$\pi _{- }+ p \rightarrow K_0 + \Sigma_0$$
$$\pi _{- }+ p \rightarrow K_+ + \Sigma_-$$
$$\pi _{+}+ p \rightarrow K_+ + \Sigma_+$$
To do this, I argue that...
Homework Statement
Let B1={([u][/1]),([u][/2]),([u][/3])}={(1,1,1),(0,2,-1),(1,0,2)} and
B2={([v][/1]),([v][/2]),([v][/3])}={(1,0,1),(1,-1,2),(0,2,1)}
a) Show that B1 is a basis for [R][/3]
b) Find the coordinates of w=(2,3,1) relative to B1
c)Given that B2 is a basis for [R[/3], find...
Homework Statement
The Matrix P =
1 0 3
1 1 0
0 3 1
is the transition matrix from what basis B to the basis B' = {(1,0,0),(1,1,0),(1,1,1) for R3?
Homework Equations
[v]B=P[v]B'
The Attempt at a Solution
I'm looking...
Not really sure how to get started on this one:Find the long-term proportions, a and b, of the two states, A and B, corresponding to the transition matrix T=|0.7 0.4|
| 0.3 0.6|
Note, the matric is a 2x2 matrix
Thanks
Hi, I am having trouble with the following question, I've answered part a but I am not sure about part b:
Suppose each year 20% of people who live in the country move into the city, while 10% of the city people move into the country.
a) If in 2015, 50% of the population live in the cities, what...
Homework Statement
find the state transition matrix of a time varying system where:
dX/dt = A*X
with A = [-1 , exp(-t - (t^2)/2) ; ; 0 , t] (Matlab format - sorry but its easier)
Homework Equations
How to go about solving such problems in a systematic way?
The Attempt at a Solution...
Homework Statement
Hello!
Please, take a look at the problem described in the attached file.
The question is: Explain why the transition matrix does what we want it to do.Homework Equations
The Attempt at a Solution
(sorry, I don't know yet how to type formulas)
I don't quite understand this...
Homework Statement
Prove the following theorem:
Suppose that B, C, and D are ordered bases for a nontrivial finite dimensional vector space V. let P be the transition matrix from B to C, and let Q be the transition matrix from C to D. Then QP is the transition matrix from B to D...
Homework Statement
Let So = {v1,v2,v3,v4} be a basis of the vector space V.
S= {u1,u2,u3,u4} is a set of vectors defined as follows:
u1 = 80v1 + 106v2 + 120v3 +164v4
u2 = 80v1 + 146v2 + 136v3 + 91v4
u3 = 90v1 + 143v2 + 122v3 + 70v4
u4 = 80v1 + 56v2 + 80v3 + 48v4
Find the Transition...
Homework Statement
Let So = {v1,v2,v3,v4} be basis of vector space V.
And S = {u1,u2,u3,u4} be set of vectors defined as follows:
u1 = 20v1 + 46v2 + 116v3 + 170v4
u2 = 20v1 + 86v2 + 147v3 + 174v4
u3 = 30v1 + 89v2 + 59v3 + 81v4
u4 = 15v1 + 27v2 + 12v3 + 9v4
Find transition matrix A from...
Homework Statement
B = {b1, b2, b3}
and
C = {c1, c2, c3}
are two basis's for R3 where the connection between the basis vectors are given by
b1 = -c1 + 4c2, b2 = -c1 + c2 + c3, b3 = c2 - 2c3
a) decide the transformation matric from basis B to basis C.
A vector x is given in...
Homework Statement
I want to find the transition matrix for the rational canonical form of the matrix A below.
Homework Equations
The Attempt at a Solution
Let ##A## be the 3x3 matrix
##\begin{bmatrix} 3 & 4 & 0 \\-1 & -3 & -2 \\ 1 & 2 & 1 \end{bmatrix}##
The...
1. -Find a regular transition matrix that is not time reversible, i.e., doesn't satisfy the
balance equations?
2.Pi,j=0≠Pj,ifor some i and j
My understanding from Markov Chain Monte Carlo is that for the transition matrix to be regular the matrix has to have all positives entries and each row...
Hi guys,
I'm having a little difficulty in converting a set of two bases into a transition matrix. My problem lies in the bases, because they are in polynomial form compared to your elementary coordinate form.
How would I go about finding the transitional matrix for this example...
Thanks in...
Let B and C be ordered bases for ℝn. Let P be the matrix whose columns are the vectors in B and let Q be the matrix whose columns are the vectors in C. Prove that the transition matrix from B to C equals Q-1P.
I am stuck. Here is what I have.
I know that if B is the standard basis in ℝn...
Homework Statement
Let B and C be ordered bases for ℝn. Let P be the matrix whose columns are the vectors in B and let Q be the matrix whose columns are the vectors in C. Prove that the transition matrix from B to C equals Q-1P.
Homework Equations
An ordered basis for a vector space V is...
Homework Statement
Let B = {(1,1,1),(1,2,2),(2,3,4)} be an ordered basis of R3, and let B` be the standard basis of R3.
Find the transition matrix from B to B` and use it to find the coordinates of (1,2,3)T with respect to B.
Homework Equations
The Attempt at a Solution
Is it...
Hello,
Homework Statement
D:R3[x]->R3[x] is defined thus for any p(x)=(a0)+(a1)x+(a2)x2+(a3)x3:
D(p(x)) = a1 + (2a2)x + (33)2
I am asked to find [D]B where B is the standard basis {1,x,x2,x3}
I am then asked to find the transition matrix from B to C, where C={1,1+x,x+x2,x2+x3}.
Based on these...
Homework Statement
The problem is in the attachment, but I'll try and rewrite it...
Suppose for a Markov Chain with two states, we get the following results.
1. If P0=[0 1] then P1=[.4 .6]
2. If P0=[4/11 7/11] then P0=P1=P2=...and so on.
With this information, find the transition...
Homework Statement
I have 2 bases, a = {1, x, x^2} and b = {-2 - 2x + 3x^2 , 1 + 2x - x^2 , -1 - x + 2x^2} of P2.
Find the transition matrix Pab.
How is this done??
Homework Equations
Since this is Linear Algebra, there aren't really any relevant "Equations" as such. More logic...
Homework Statement
I have 2 bases, a = {1, x, x^2} and b = {-2 - 2x + 3x^2 , 1 + 2x - x^2 , -1 - x + 2x^2} of P2.
Find the transition matrix Pab.
How is this done??Homework Equations
Since this is Linear Algebra, there aren't really any relevant "Equations" as such. More logic based...
Homework Statement
I'm enormously frustrated with these problems. I've been trying to figure out how to find out what the transition matrix between C and B is for about 2 hours and I still can't get it. I've watched 4 youtube videos and read two websites as well as the section in my...
Homework Statement
I design a markov model to study the availability of a node which will not work unless the network work: I make the following matrix. In which (i,j) means i is node up /down and j is network up/down. R1,R2 means the repair rate for node and network. F1,F2 means the failure...
Hi:
I`m new here, can someone tell me which is the difference between the transition matrix and the Jacobian?, I did some exercises of the both topics, but How is it related?
Thanks for the attention
Sorry for my English writing, but English is not my native language.
As I understand, a Markov chain transition matrix rewritten in its canonical form is a large matrix that can be separated into quadrants: a zero matrix, an identity matrix, a transient to absorbing matrix, and a transient to transient matrix.
The zero matrix and identity matrix parts are easy...
Hey folks, I have an orbit in the circular restricted three body problem with initial conditions
[x(0), 0, z(0), 0, y'(0), 0]
I'm following this paper
http://adsabs.harvard.edu/full/1984CeMec..32...53H
on how to correct these initial conditions given the state transition matrix at a...
hi ,
I need to create a program on mathématica 8 to study the stability of my system using Floquet transition matrix .
to compute the Floquet transition matrix I made this program based on a fourth order Runge Kutta integration :
X1[t_] = {x1[t], x2[t], x3[t], x4[t], x5[t], x6[t] ...
Homework Statement
The total population size is N = 5, of which some are diseased and the rest are healthy. During any single period of time, two people are selected at random from the population and assumed to interact. The selection is such that an encounter between any pair of individuals...
Homework Statement
Given a Probability transition matrix, starting in X0= 1, determine the probability that the process never reaches state 2.
Homework Equations
The Attempt at a Solution
State 2 is not an observing state, so I'm not sure how to find this probability.
Any help...
Homework Statement
I am trying to find the state transition matrix of a 5x5 matrix. Is there a way to use MATLAB in this problem ?
Homework Equations
\Phi = (T^-1) x e^(Dt) x T
Where D is 5x5 matrix containing the eigenvalues in the main diagonal, rest of elements are zeros.
T...
Homework Statement
Hi all,
I've the following problem: I've a series of correlations matrices, suppose 15x15 matrix of correlations between waves heights. Giving an historical series of correlation values, how can I determine a model to establish that the next correlation matrix has a...
If a Markov transition matrix's columns add up to 1, the matrix is a normal Markov transition matrix. Since it is normal, the Markov process must converge to a steady-state vector.
Is this correct?