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Matrices and applications — Question 199

Original QCE Vault practice · 5 marks

Q199 · Practice questionTechnology-freeComplex unfamiliar5 marks

QUESTION 199 (5 marks)

A population follows

\binom{J_{n+1}}{A_{n+1}}=\begin{pmatrix}0&f\\0.4&0.6\end{pmatrix}\binom{J_n}{A_n}

with f>0.

a)

Determine f and the positive stage ratio for a vector unchanged every step.

[3 marks]

b)

For f=1.5 and initial vector (100,100), find total expected population after two steps.

[2 marks]

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