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In a certain city, the Democratic, Republican, and Consumer parties always nominate candidates for mayor. The probability of winning in any election depends on the party in power and is given by the following transition matrix.
Using the given transition matrix and assuming the initial-probability vector is , find the probability vector for the fourth stage of the Markov chain. (This initial-probability vector indicates that a Consumer is certain to win the initial election.)
Multiple Languages
The ability or system to use, understand, or incorporate more than one language, often in the context of programming, communication, or learning.
Transacting Business
The act of conducting trade or commerce between parties, including selling, buying, and exchanging goods, services, or information.
Environmental Clean-Up
The process of removing pollution or contaminants from environmental media such as soil, groundwater, sediment, or surface water for the general protection of the environment.
Sustainability
The ability to maintain healthy environmental, social, and economic systems in balance, indefinitely, ensuring a quality of life for future generations.
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