Here's the question from the newest version of ASM:
The solution uses the binomial random variable shortcut to get an answer of 17.16
Can someone explain how to do this without using the shortcut? I get 22 lives are expected to die within the first two years, so E[X] = 22? But then when it comes to calculating E[X^2] I screw up.
Any help would be appreciated.
Quote:
For a multi-state model with three states, healthy (0), disabled (1), and dead (2): The transition matrix is .70 .20 .10 .10 .65 .25 .00 .00 1.0 There are 100 lives at the start, all healthy. Their future states are independent. Calculate the variance of the number of the original 100 lives who die within the first two years. |
The solution uses the binomial random variable shortcut to get an answer of 17.16
Can someone explain how to do this without using the shortcut? I get 22 lives are expected to die within the first two years, so E[X] = 22? But then when it comes to calculating E[X^2] I screw up.
Any help would be appreciated.
ASM 43.8
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