Homework Answers
(a). v = P.p0 = (9/20,11/20)T.
(b). The steady state vector v is given by Pv = v or, (P-I2)v = 0. To solve this equation, we have to reduce P-I2 to its RREF which is
|
1 |
-4/5 |
|
0 |
0 |
Now, if v = (v1,v2)T, then the equation (P-I2)v = 0 is equivalent to v1-4v2/5 = 0 or, v1 = 4v2/5. Then v = (4v2/5,v2)T .
If 4v2/5 + v2 = 1, then v2* (9/5) = 1 or, v2 = 5/9 so that v1 = (4/5)*(5/9) = 5=4/9. and v =(v1,v2)T = ( 4/9,5/9)T.
Thus, v = ( 4/9,5/9)T.
Add Answer to:
0.5 0. and a probability Bonus. Consider a Markor chain with two states, an initial probability v...
-1:1 0.5 0.7 0.5 be the transition matrix for a Markov chain with two states. Let...
-1:1 0.5 0.7 0.5 be the transition matrix for a Markov chain with two states. Let x be the initial state vector for the population. 0.5 0.3 0.5 Find the steady state vector x. (Give the steady state vector as a probability vector.) x= Need Help?Read It Talk to a Tutor
0.5 0 0 5. Let P 0.5 0.6 0.3represent the probability transition matrix of a Markov...
0.5 0 0 5. Let P 0.5 0.6 0.3represent the probability transition matrix of a Markov chain with three 0 0.4 0.7 states (a) Show that the characteristic polynomial of P is given by P-ÀI -X-1.8λ2 +0.95λ-0.15) (b) Verify that λι 1, λ2 = 0.5 and λ3 = 0.3 satisfy the characteristic equation P-λ1-0 (and hence they are the eigenvalues of P) c) Show thatu3u2and u3are three eigenvectors corresponding to the eigenvalues λι, λ2 and λ3, respectively 1/3 (d) Let...
Let Xn be a Markov chain with state space {0,1,2}, the initial probability vector and one step transition matrix a. Co...
Let Xn be a Markov chain with state space {0,1,2}, the initial
probability vector and one step transition matrix
a. Compute.
b. Compute.
3. Let X be a Markov chain with state space {0,1,2}, the initial probability vector - and one step transition matrix pt 0 Compute P-1, X, = 0, x, - 2), P(X, = 0) b. Compute P( -1| X, = 2), P(X, = 0 | X, = 1) _ a.
3. Let X be a Markov chain...
Please Show All work I have been stuck on these two questions for the last few days and can't see...
Please Show All work I have been stuck on these two
questions for the last few days and can't seem to get it right
:(
3. 0/1 points | Previous Answers PooleLinAlg4 3.7.004 Let p 0.5 0.7 0.5 0.3 0.5 0.5 be the transition matrix for a Markov chain with two states. Let x be the initial state vector for the population Find the steady state vector x. (Give the steady state vector as a probability vector.) 5834 4107 Need...
An absorbing Markov Chain has 5 states where states #1 and #2 are absorbing states and the following transition probabilities are known: p3,2=0.1, p3, 3=0.4, p3,5=0.5 p4,1=0.1, p4,3=0.5, ...
An absorbing Markov Chain has 5 states where states #1 and #2 are absorbing states and the following transition probabilities are known: p3,2=0.1, p3, 3=0.4, p3,5=0.5 p4,1=0.1, p4,3=0.5, p4,4=0.4 p5,1=0.3, p5,2=0.2, p5,4=0.3, p5,5 = 0.2 (a) Let T denote the transition matrix. Compute T3. Find the probability that if you start in state #3 you will be in state #5 after 3 steps. (b) Compute the matrix N = (I - Q)-1. Find the expected value for the number of...
1. Let {Xt,t 0,1,2,...J be a Markov chain with three states (S 1,2,3]), initial distribution (0.2,0.3,0.5)...
1. Let {Xt,t 0,1,2,...J be a Markov chain with three states (S 1,2,3]), initial distribution (0.2,0.3,0.5) and transition probability matrix P0.5 0.3 0.2 0 0.8 0.2 (a) Find P(Xt+2 1, Xt+1-2Xt 3) (b) Find the two step transition probability matrix P2) and specifically (e) Find P(X2-1 (d) Find EXi.
(n)," 2 0) be the two-state Markov chain on states (. i} with transition probability matrix...
(n)," 2 0) be the two-state Markov chain on states (. i} with transition probability matrix 0.7 0.3 0.4 0.6 Find P(X(2) 0 and X(5) X() 0)
Consider the Markov chain with the following transition diagram. 1 0.5 0.5 0.5 0.5 0.5 2 3 0.5 (a) Write down the trans...
Consider the Markov chain with the following transition diagram. 1 0.5 0.5 0.5 0.5 0.5 2 3 0.5 (a) Write down the transition matrix of the Markov chain (b) Compute the two step transition matrix of the Markov chain 2 if the initial state distribution for 2 marks (c) What is the state distribution T2 for t t 0 is To(0.1, 0.5, 0.4)7? [3 marks (d) What is the average time 1.1 for the chain to return to state 1?...
Let Xn be a Markov chain with state space {0, 1, 2}, and transition probability matrix...
Let Xn be a Markov chain with state space {0, 1, 2}, and transition probability matrix and initial distribution π = (0.2, 0.5, 0.3). Calculate P(X1 = 2) and P(X3 = 2|X0 = 0) 0.3 0.1 0.6 p0.4 0.4 0.2 0.1 0.7 0.2
Q.4 [8 marks] Consider the Markov chain with the following transition diagram 1 0.5 0.5 0.5 0.5 0.5 2 3 0.5 (a) Write d...
Q.4 [8 marks] Consider the Markov chain with the following transition diagram 1 0.5 0.5 0.5 0.5 0.5 2 3 0.5 (a) Write down the transition matrix of the Markov chain 1 marks 2 marks (b) Compute the two step transition matrix of the Markov chain (c) What is the state distribution T2 for t = 2 if the initial state distribution for 2 marks t 0 is o (0.1, 0.5, 0.4)T? 3 marks (d) What is the average time...
-1:1 0.5 0.7 0.5 be the transition matrix for a Markov chain with two states. Let x be the initial state vector for the population. 0.5 0.3 0.5 Find the steady state vector x. (Give the steady state vector as a probability vector.) x= Need Help?Read It Talk to a Tutor
0.5 0 0 5. Let P 0.5 0.6 0.3represent the probability transition matrix of a Markov chain with three 0 0.4 0.7 states (a) Show that the characteristic polynomial of P is given by P-ÀI -X-1.8λ2 +0.95λ-0.15) (b) Verify that λι 1, λ2 = 0.5 and λ3 = 0.3 satisfy the characteristic equation P-λ1-0 (and hence they are the eigenvalues of P) c) Show thatu3u2and u3are three eigenvectors corresponding to the eigenvalues λι, λ2 and λ3, respectively 1/3 (d) Let...
Let Xn be a Markov chain with state space {0,1,2}, the initial
probability vector and one step transition matrix
a. Compute.
b. Compute.
3. Let X be a Markov chain with state space {0,1,2}, the initial probability vector - and one step transition matrix pt 0 Compute P-1, X, = 0, x, - 2), P(X, = 0) b. Compute P( -1| X, = 2), P(X, = 0 | X, = 1) _ a.
3. Let X be a Markov chain...
Please Show All work I have been stuck on these two
questions for the last few days and can't seem to get it right
:(
3. 0/1 points | Previous Answers PooleLinAlg4 3.7.004 Let p 0.5 0.7 0.5 0.3 0.5 0.5 be the transition matrix for a Markov chain with two states. Let x be the initial state vector for the population Find the steady state vector x. (Give the steady state vector as a probability vector.) 5834 4107 Need...
1. Let {Xt,t 0,1,2,...J be a Markov chain with three states (S 1,2,3]), initial distribution (0.2,0.3,0.5) and transition probability matrix P0.5 0.3 0.2 0 0.8 0.2 (a) Find P(Xt+2 1, Xt+1-2Xt 3) (b) Find the two step transition probability matrix P2) and specifically (e) Find P(X2-1 (d) Find EXi.
(n)," 2 0) be the two-state Markov chain on states (. i} with transition probability matrix 0.7 0.3 0.4 0.6 Find P(X(2) 0 and X(5) X() 0)
Consider the Markov chain with the following transition diagram. 1 0.5 0.5 0.5 0.5 0.5 2 3 0.5 (a) Write down the transition matrix of the Markov chain (b) Compute the two step transition matrix of the Markov chain 2 if the initial state distribution for 2 marks (c) What is the state distribution T2 for t t 0 is To(0.1, 0.5, 0.4)7? [3 marks (d) What is the average time 1.1 for the chain to return to state 1?...
Q.4 [8 marks] Consider the Markov chain with the following transition diagram 1 0.5 0.5 0.5 0.5 0.5 2 3 0.5 (a) Write down the transition matrix of the Markov chain 1 marks 2 marks (b) Compute the two step transition matrix of the Markov chain (c) What is the state distribution T2 for t = 2 if the initial state distribution for 2 marks t 0 is o (0.1, 0.5, 0.4)T? 3 marks (d) What is the average time...
Most questions answered within 3 hours.
-
After watching the lectures I am still having a hard time
understanding these equations.
1. The...
asked 20 minutes ago -
Testing:
H0:μ=56.9
H1:μ<56.9
Your sample consists of 23 subjects, with a mean of 56.3 and
standard...
asked 23 minutes ago -
straight wire, labeled as Wire A, lies horizontally on a
tabletop and is oriented to run...
asked 24 minutes ago -
For a Chi-Squared Goodness of Fit Test about a uniform
distribution, complete the table.
Round to...
asked 52 minutes ago -
Milk of magnesia is only slightly soluble in water. Kc for the
reaction Mg(OHs)(s)>Mg2+(a) + 2OH-1(aq)...
asked 47 minutes ago -
Excel's HYPGEOM.DIST function can be used to compute _____.
a. both hypergeometric probabilities and cumulative
hypergeometric...
asked 1 hour ago -
The rocket used for the human lunar missions was the Saturn V
rocket. At liftoff the...
asked 49 minutes ago -
1. The East Street Bagel Shop has a weekly demand for 3,500
bagels, which they make...
asked 52 minutes ago -
paraphrasing each paragraph
“Where two or more persons knowingly act together unlawfully,
the act of each...
asked 1 hour ago -
The lateral line system in fish is contained which of the
following?
chemoreceptors
photoreceptors
mechanoreceptors
odor...
asked 1 hour ago -
Find the y-intercept of y =-5 x. The y-intercept of y equals
negative 5 x is______...
asked 1 hour ago -
Customers arrive randomly at a gas station at the average rate
of 30 per hour, while...
asked 1 hour ago