Question

Suppose in Florida it was observed that 70% of parents who were vegetarian were succeeded by children who were vegetarian and 30% by non-vegetarian. Also, 40% of non-vegetarians were succeeded by vegetarians and 60% by non-vegetarians. Set up the 2x2 stochastic matrix with columns and rows labeled V and NV that describes this situation.
V NV
A. V 0.7 0.4
NV 0.3 0.6
V NV
B. V 0.4 0.7
NV 0.3 0.6
V NV
C. V 0.7 0.4
NV 0.7 0.6
V NV
D. V 0.6 0.3
NV 0.3 0.4

Answer 1

Answer:

A

Step-by-step explanation:

From the information given:

To create the required stochastic matrix, we need to take parents who are shown to be vegetarian or nonvegetarian in the column and the children who are vegetarian or nonvegetarian into the row section.

So;

Vegetarian V → 70% →            nonvegetarian NV → 30%

nonvegetarian NV → 40%             vegetarian    V →  60%

                                                           V     NV

The 2x2 stochastic matrix  =     $\left \Big { {{V} \atop {NV}} \right.} \left [\begin{array} {cc}0.7&0.4\\0.3&0.6\\\end{array}\right]$