Question

A laboratory animal may eat any one of three foods each day. Laboratory records show that if the animal chooses one food on one trial, it will choose the same food on the next trial with a probability of 50%, and it will choose the other foods on the next trial with equal probabilities of 25%. What is the stochastic matrix for this situation?

Answer 1

`P= \left[\begin{array}{ccc}0.5&0.25&0.25\\0.25&0.5&0.25\\0.25&0.25&0.5\end{array}\right]`

Explanation:

let a, b and c be the type of foods used in trail.

Example matrix combination for (1,1) is (a,a) is 0.5. Another Example for (1,2) is (a,b) is 0.25.

The diagonals are (a,a), (b,b) and (c,c) which means same food in two trails and its probability is 0.5. the rest would be 0.25

Therefore, stochastic matrix would have 3 by 3 matrix such as (a,a), (a,b) .... (c,c)

`\left[\begin{array}{ccc}0.5&0.25&0.25\\0.25&0.5&0.25\\0.25&0.25&0.5\end{array}\right] \\`