Finite Mathematics covers mathematical concepts and techniques applicable to business and social sciences, including matrix algebra, linear programming, and probability.
Markov chains model situations where the next state depends only on the current state, not how you got there. Each state transitions to another with a certain probability.
We use matrices to represent the probabilities of moving from one state to another. After several steps, we can predict the likelihood of being in any state.
Markov chains are used in economics, board games, customer behavior prediction, and even Google's PageRank algorithm!
\[ \mathbf{P}_{n+1} = \mathbf{P}_n \times \mathbf{T} \] where \(\mathbf{P}_n\) is the probability vector at step \(n\), and \(\mathbf{T}\) is the transition matrix.
\[\mathbf{P}_{n+1} = \mathbf{P}_n \times \mathbf{T}\]
Predicting how a customer moves between being a browser and a buyer on a website.
Modeling board game moves where each roll depends only on the current square.
Markov chains predict future events based on current information using transition probabilities.