Question

In: Statistics and Probability

Consider the following Markov chain: 0 1 2 3 0 0.3 0.5 0 0.2 1 0.5...

Consider the following Markov chain:

0

1

2

3

0

0.3

0.5

0

0.2

1

0.5

0.2

0.2

0.1

2

0.2

0.3

0.4

0.1

3

0.1

0.2

0.4

0.3

  1. What is the probability that the first passage time from 2 to 1 is 3?
  2. What is the expected first passage time from 2 to 1?
  3. What is the expected first passage time from 2 to 2 (recurrence time for 2)? What is the relation between this expectation and the steady-state probability of being at state 2?

Solutions

Expert Solution


Related Solutions

Mg standard Absorbance %RSD 0.5 0.09533 0.3 1 0.1209 0.2 2 0.17304 0.3 5 0.28137 0.2...
Mg standard Absorbance %RSD 0.5 0.09533 0.3 1 0.1209 0.2 2 0.17304 0.3 5 0.28137 0.2 10 0.56901 0.5 20 0.87153 0.3 5 mL Unk 0.14296 0.2 [1] Make a calibration curve using the absorbances for the samples from 0.5 – 20 ppm. Include the intercept (0,0) as a data point. [2] Is the calibration linear, i.e., does the analysis follow Beer’s law? To discuss linearity, examine both the trend of the data relative to the least squares line and...
x −4 −3 −2 −1 0 P(X=x) 0.2 0.1 0.3 0.2 0.2 Step 1 of 5:...
x −4 −3 −2 −1 0 P(X=x) 0.2 0.1 0.3 0.2 0.2 Step 1 of 5: Find the expected value E(X). Round your answer to one decimal place. Step 2 of 5: Find the variance. Round your answer to one decimal place. Step 3 of 5: Find the standard deviation. Round your answer to one decimal place. Step 4 of 5: Find the value of P(X>−1)P(X>−1). Round your answer to one decimal place. Step 5 of 5: Find the value...
Consider a Markov chain {Xn|n ≥ 0} with state space S = {0, 1, · ·...
Consider a Markov chain {Xn|n ≥ 0} with state space S = {0, 1, · · · } and transition matrix (pij ) given by pij = 1 2 if j = i − 1 1 2 if j = i + 1, i ≥ 1, and p00 = p01 = 1 2 . Find P{X0 ≤ X1 ≤ · · · ≤ Xn|X0 = i}, i ≥ 0 . Q2. Consider the Markov chain given in Q1. Find P{X1,...
The following is the transition probability matrix of a Markov chain with states 1, 2, 3,...
The following is the transition probability matrix of a Markov chain with states 1, 2, 3, 4 P 0 1 2 3 0 .4 .3 .2 .1 1 .2 .2 .2 .4 2 .25 .25 .5 0 3 .2 .1 .4 .3 If Xnot = 1 (a) find the probability that state 3 is entered before state 4; (b) find the mean number of transitions until either state 3 or state 4 is entered.
Let {Xn|n ≥ 0} is a Markov chain with state space S = {0, 1, 2,...
Let {Xn|n ≥ 0} is a Markov chain with state space S = {0, 1, 2, 3}, and transition probability matrix (pij ) given by   2 3 1 3 0 0 1 3 2 3 0 0 0 1 4 1 4 1 2 0 0 1 2 1 2   Determine all recurrent states. Q3. Let {Xn|n ≥ 0} is a Markov chain with state space S = {0, 1, 2} and transition probability matrix (pij...
x 0 1 2 3 4 P(X) 0.45 0.3 0.2 0.04 0.01 (a) Find and interpret...
x 0 1 2 3 4 P(X) 0.45 0.3 0.2 0.04 0.01 (a) Find and interpret the expected value of X (b)Find the variance of X (c)Find the probability that a person has 1 sibling given that they have less than 3 siblings. (d)Find the probability that a person has at least 1 sibling OR less than 2 siblings
Consider the following data: x -4 -3 -2 -1 0 P(X=x) 0.2 0.1 0.2 0.1 0.4...
Consider the following data: x -4 -3 -2 -1 0 P(X=x) 0.2 0.1 0.2 0.1 0.4 Step 2 of 5 : Find the variance. Round your answer to one decimal place. Step 3 of 5 : Find the standard deviation. Round your answer to one decimal place.
Correlations: -0.9, -0.5, -0.2, 0, 0.2, 0.5, and 0.9. For each, give the fraction of the...
Correlations: -0.9, -0.5, -0.2, 0, 0.2, 0.5, and 0.9. For each, give the fraction of the variation in Y that is explained by the least- squares regression of Y on X. Summarize what you have found from performing these calculations.
X 1 2 3 4 5 P(X) 0.2 0.3 0.1 0.3 a) Finish the probability table...
X 1 2 3 4 5 P(X) 0.2 0.3 0.1 0.3 a) Finish the probability table b) Define Y = -2X+6 . c) Calculate E(X) Std(X) E(Y) Std(Y)
Xn is a Markov Chain with state-space E = {0, 1, 2}, and transition matrix 0.4...
Xn is a Markov Chain with state-space E = {0, 1, 2}, and transition matrix 0.4 0.2 0.4 P = 0.6 0.3 0.1 0.5 0.3 0.2 And initial probability vector a = [0.2, 0.3, 0.5] For the Markov Chain with state-space, initial vector, and transition matrix discuss how we would calculate the follow; explain in words how to calculate the question below. a) P(X1 = 0, X2 = 0, X3 = 1, X4 = 2|X0 = 2) b) P(X2 =...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT