The daily price of a farm commodity is up, down, or unchanged from the day befor

Question

The daily price of a farm commodity is up, down, or unchanged from the day before. Analysts predict that if the last price was down, there is a .5 probability the next will be down, and a .4 probability the price will be unchanged. If the last price was unchanged, there is a .35 probability it will be down and a .35 probability it will be up. For prices whose last movement was up, the probabilities of down, unchanged, and up are .1, .3, and .6.

            a.         Construct the matrix of transition probabilities.

            b.         Provide (but do not solve) a system of equations for calculating the steady state probabilities.

Explanation / Answer

Combinatorics is a sub-discipline of Algebra which is concerned with the study of combination, enumeration and permutation ofsets of elements. One of the main aspects of combinatorics is the study of combinatorial structures found in an algebraic context. It draws on principles from Group Theory and Representation Theory.

Representation Theory is the study of abstract algebraic structures. It aims to represent their elements in the form of linear transformations of vector spaces; in essence, representation makes an abstract mathematical concept more concrete. Thus, it can be seen that this particular theory is especially prominent in the study of Combinatorics

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