Three white and three black balls are distributed in two urns in such a way that each urncontains three balls. We say the system is in state i (i = 0, 1, 2, 3) if the first urn contains i whiteballs. At each step, we draw one ball firom each urn and place the ball drawn from the first urninto the second, and conversely with the ball from the second urn. Let X, denote the state of thesystem after the nth step. Specify the transition probability matrix for the Markov chain {Xn}.

*Answer: There are 3 white balls and 3 black balls, which are distributed in two urns such that…

Answered: white and three black balls are…

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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A rainy year is 80% likely to be followed by a rainy year and a drought is 60% likely to be followed by another drought year. Suppose the rainfall condition is known for the initial year to be ‘rainy’. Then the vector ? 0 = 10 gives probabilities of rainy and drought for known initial year.(a) Write out the stochastic matrix.(b) Find the probabilities for:(i) Year 1(ii)
The four brands of soap have the current market share of 0.23, 0.28, 0.25, and 0.24 for brands A, B, C, and D, respectively. Below are the transition probability matrix of the soap brands based on their annual performance and the number of customers using the brands. 0.4 2300 T 0.3 2800 0.2 2500 2400 From/To A B C D A 0.2 0 0.3 0.3 B 0.3 0.2 0.5 0.4 C 0.1 0.5 0 0.3 D 0 a) What is the market share of Brand D in the long run? Answer in 2 decimal places. c) What is the mean return time of Brand A? Answer in 2 decimal places. b) How many customers will shift preference in using Brand C soap in the long run? Number of Customers d) What is the percentage change of Brand B? Answer in percentage and in 2 decimal places.
Use a software program or a graphing utility with matrix capabilities to find the transition matrix from B to B'. B = {(2, 5), (1, 2)}, B' = {(-1, 10), (-1,5)} ↓ 1 Need Help? Read It Watch It
A study of armed robbers yielded the approximate transition probability matrix shown below. The matrix gives the probability that a robber currents free, on probation, or in jail would, over a period of a year, make a transition to one of the states. То From Free Probation Jail Free 0.7 0.2 0.1 Probation 0.3 0.5 0.2 Jail 0.0 0.1 0.9 Assuming that transitions are recorded at the end of each one-year period: i) For a robber who is now free, what is the expected number of years before going to jail? ii) What proportion of time can a robber expect to spend in jail? [Note: You may consider maximum four transitions as equivalent to that of steady state if you like.]
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Given data points (2,-1), (2, 1), (3,2), (0,-1), and (3,-1), compute the sample covariance matrix. Record the entries of covariance matrix row by row as decimal numbers, separated by commas.

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