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Part III: Microeconomics: The Science of Consumer and Firm Behaviour
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We can replace the original owgraph with the one shown in Figure 2.17, a owgraph that has two paths in parallel. The survival time of a patient in state 0 is now a nite mixture distribution: With probability 2 /( 1 + 2 ) it is Exp( 1 + 2 ), and with probability 1 /( 1 + 2 ) it is the convolution of an Exp( 1 + 2 ) with an independent Exp( 3 ), the passage time from state 1 to 2. The MGF of the time to death is M(s) = 2 1 + 2 1 + 2 1 + 2 s + 1 1 + 2 1 + 2 1 + 2 s 3 3 s (2.16)
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