Hamsters at a pet shop can either be Healthy (State 0), Injured (State 1), or Dead (State 2). Hamsters can transition both ways between State 0 and State 1, but cannot move out of State 2 once in that state. You are given the following constant forces of transition: (i) μ01 = 0.03 (ii) ¹0 = 0.08 (iii) 02 = 0.01 (iv) ¹2 = 0.09 Calculate the probability that an injured hamster on Jan 1, 2012 will become healthy before the end of the year, but will not remain continuously healthy until the end of the year. C. 0.0155 A. 0.0015 B. 0.0063 Hint: Make a time diagram, write corresponding integral. D. 0.0449 E. 0.0721

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Chapter1: Combinatorial Analysis
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Hamsters at a pet shop can either be Healthy (State 0), Injured (State 1), or Dead (State 2). Hamsters
can transition both ways between State 0 and State 1 , but cannot move out of State 2 once in that
state. You are given the following constant forces of transition:
(i) µ01 = 0.03
(ii) µ10 = 0.08
(iii) µ02 = 0.01
(iv) µ12 = 0.09
Calculate the probability that an injured hamster on Jan 1, 2012 will become healthy before the end
of the year, but will not remain continuously healthy until the end of the year.
A. 0.0015
B. 0.0063
C. 0.0155
D. 0.0449
E. 0.0721
Hint: Make a time diagram, write corresponding integral.
Transcribed Image Text:Hamsters at a pet shop can either be Healthy (State 0), Injured (State 1), or Dead (State 2). Hamsters can transition both ways between State 0 and State 1 , but cannot move out of State 2 once in that state. You are given the following constant forces of transition: (i) µ01 = 0.03 (ii) µ10 = 0.08 (iii) µ02 = 0.01 (iv) µ12 = 0.09 Calculate the probability that an injured hamster on Jan 1, 2012 will become healthy before the end of the year, but will not remain continuously healthy until the end of the year. A. 0.0015 B. 0.0063 C. 0.0155 D. 0.0449 E. 0.0721 Hint: Make a time diagram, write corresponding integral.
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