3. The victims of a certain disease are classified into three states: cured, dead from the disease, or sick. Once a person is cured, he is permanently immune. Each year, 70% of those sick are cured, 10% die from the disease and 20% remain ill. (a) Create a transition diagram that describes this scenario. (b) Create a stochastic matrix that describes this scenario. Is this scenario ergodic or absorbing? Explain. (c) Rewrite the matrix in standard form.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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3. The victims of a certain disease are classified into three states: cured, dead from the
disease, or sick. Once a person is cured, he is permanently immune. Each year, 70%
of those sick are cured, 10% die from the disease and 20% remain ill.
(a) Create a transition diagram that describes this scenario.
(b) Create a stochastic matrix that describes this scenario. Is this scenario ergodic
or absorbing? Explain.
(c) Rewrite the matrix in standard form.
(d) Find N, R and B.
(e) On average, if a person begins as healthy, how long will a person remain ill before
being cured or passing away?
(f) Determine the probability that a person will be cured if they begin as ill.
(g) Determine the probability that a person will die if they begin as healthy.
Transcribed Image Text:3. The victims of a certain disease are classified into three states: cured, dead from the disease, or sick. Once a person is cured, he is permanently immune. Each year, 70% of those sick are cured, 10% die from the disease and 20% remain ill. (a) Create a transition diagram that describes this scenario. (b) Create a stochastic matrix that describes this scenario. Is this scenario ergodic or absorbing? Explain. (c) Rewrite the matrix in standard form. (d) Find N, R and B. (e) On average, if a person begins as healthy, how long will a person remain ill before being cured or passing away? (f) Determine the probability that a person will be cured if they begin as ill. (g) Determine the probability that a person will die if they begin as healthy.
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