A Markov chain has the transition matrix shown below: 0.8 0.2 P = 0.3 0.7] (Note: For questions 1, 2, and 4, express your answers as decimal fractions rounded to 4 decimal places (if they have more than 4 decimal places).) (1) If, on the first observation the system is in state 1, what is the probability that it is in state 1 on the second observation? ... ... ... (2) If, on the first observation the system is in state 1, what is the probability that it is in state 1 on the third observation? ... (3) If, on the first observation, the system is in state 2, what state is the system most likely to occupy on the third observation? (If there is more than one such state, which is the first one.) ... ...

A Markov chain has the transition matrix shown below: 0.8 0.2 P = 0.3 0.7] (Note: For questions 1, 2, and 4, express your answers as decimal fractions rounded to 4 decimal places (if they have more than 4 decimal places).) (1) If, on the first observation the system is in state 1, what is the probability that it is in state 1 on the second observation? ... ... ... (2) If, on the first observation the system is in state 1, what is the probability that it is in state 1 on the third observation? ... (3) If, on the first observation, the system is in state 2, what state is the system most likely to occupy on the third observation? (If there is more than one such state, which is the first one.) ... ...

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...

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c. The market share of two companies A and B is 30% and 70% in the current time period. The information obtained in terms of the customer loss and retention is given by the matrix P. [0.3 0.2] P = Lo.7 0.8] i.Determine the transition probability matrix in the 1st and 2nd month. ii.What is the steady state of the two companies?
The following data consists of a matrix of transition probabilities (P) of three competing companies, the initial market share state ℼ(1), and the equilibrium probability states. Assume that each state represents a firm (Company 1, Company 2, and Company 3, respectively) and the transition probabilities represent changes from one month to the next. The market share of Company 3 after three periods is a. 0.259 b. 0.261 c. 0.283 d. 0.296
Consider the Markov chain specified by the following transition diagram. a. Find the steady-state probabilities of all states. 0.4 b. If the initial state is 7, what is the expected 0.3 0.4 0.2 number of steps to reach state 1 or 3? 0.8 0.2 c. If at step 0 the system was in state 4, what is the probability that after step 3 it was in state 3 and after step 47 it was in state 3 again?
On each of three consecutive days the National Weather Service announces that there is a 50-50 chance of rain. Assuming that the National Weather Service is correct, what is the probability that it rains on at most one of the three days? Justify your answer. (Hint: Represent the outcome that it rains on day 1 and doesn’t rain on days 2 and 3 as RNN.)
The following data consists of a matrix of transition probabilities (P) of three competing companies, the initial market share state ℼ(1), and the equilibrium probability states. Assume that each state represents a firm (Company 1, Company 2, and Company 3, respectively) and the transition probabilities represent changes from one month to the next. The market share of Company 2 after two periods is a. 0.283 b. 0.26 c. 0.261 d. 0.47
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60. The following is the transition probability matrix of a Markov chain with states 1, 2, 3, 4 P= .4 .2 .25 .2 .3 .2 .1 .2 .2 .4 25 50 .1 .4 .3 If Xo = 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.
Please do the following questions with handwritten working out. Answer is in other image
Can someone please help me with this question. I am having so much trouble.
Milan.stt
A Markov chain has the transition matrix shown below: 0.2 0.1 0.7] P = 0.6 0.4 1 (Note: For questions 1, 3, and 5, express your answers as decimal fractions rounded to 4 decimal places (if they have more than 4 decimal places).) (1) If, on the first observation the system is in state 1, what is the probability that it is in state 1 on the next observation? (2) If, on the first observation the system is in state 1, what state is the system most likely to occupy on the next observation? (If there is more than one such state, which is the first one.) (3) If, on the first observation, the system is in state 1, what is the probability that the system is in state 1 on the third observation? ...