The Matrix of Transition Probabilities Below Deals with Brand Loyalty

question 10

Essay

The matrix of transition probabilities below deals with brand loyalty to Bark Bits and Canine Chow dog food. $$\begin{array} { c | c c } \text { Current } & { \text { Next Purchase } } \\\text { Purchase } & \text { Bark Bits } & \text { Canine Chow } \\\hline \text { Bark Bits } & .75 & .25 \\\text { Canine Chow } & .20 & .80\end{array}$$
a.What are the steady state probabilities?
b.What is the probability that a customer will switch brands on the next purchase after a large number of periods?

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Definitions:

Branching Tubes

Refers to the structures found in organisms, such as the respiratory and vascular systems, that divide and subdivide into smaller tubes.

Capillary Network

An intricate network of capillaries, the smallest blood vessels, facilitating the exchange of water, oxygen, carbon dioxide, and many other nutrients and waste substances between blood and tissues.

Metanephridia

Excretory organs found in some invertebrates, such as annelid worms, that help in the removal of metabolic wastes.

Tubule

A small tube or tubular structure, especially in biological contexts, such as the renal tubules in kidneys.