In this lesson, we will learn how to use a matrix to represent probabilities.

Q1:

On any given day, an animal eats either cheese, grapes, or lettuce. The food the animal eats is influenced by the food it ate the previous day:

Represent these probabilities in the matrix 𝑃, where the columns, in order, represent the events of eating cheese, grapes, or lettuce tomorrow; and the rows, in order, represent the events of eating cheese, grapes, or lettuce today.

Letting 𝑄=𝑃, what is the interpretation of the entry 𝑄?

Q2:

What does it mean for a matrix 𝐴=(𝑎) to be stochastic?

Q3:

Under which of the following conditions is the 𝑛×𝑛 matrix 𝐴=(𝑎) a Markov matrix?

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