Question

(b) Consider a permanent disability model where $\mu_x^{02} = \mu_x^{12}$ for all x. (i) Show that $\bar{p}_{x}^{00} \bar{p}_{x+t}^{11} = e^{-\int_0^t \mu_{x+s}^{01} ds} e^{-\int_0^t \mu_{x+s}^{02} ds}$. (ii) Given that $\mu_x^{01} = 0.3$ and $\mu_x^{02} = 0.1$, find the probability of transitioning from State 0 to State 1 exactly once and staying in State 1 until time 5.

          (b) Consider a permanent disability model where $\mu_x^{02} = \mu_x^{12}$ for all x.

(i) Show that $\bar{p}_{x}^{00} \bar{p}_{x+t}^{11} = e^{-\int_0^t \mu_{x+s}^{01} ds} e^{-\int_0^t \mu_{x+s}^{02} ds}$.

(ii) Given that $\mu_x^{01} = 0.3$ and $\mu_x^{02} = 0.1$, find the probability of transitioning from State 0 to State 1 exactly once and staying in State 1 until time 5.

(b) Consider a permanent disability model where ^02 = ^12 for all x.

(i) Show that p̅x^00p̅x+t^11 = e^-∫0^t μx+s^01 ds e^-∫0^t μx+s^02 ds.

(ii) Given that ^01 = 0.3 and ^02 = 0.1, find the probability of transitioning from State 0 to State 1 exactly once and staying in State 1 until time 5.

Added by David C.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Rashmi Sinha

Step 1

The probability of transitioning from State 0 to State 1 exactly once can be calculated using the formula for a geometric distribution. In this case, the probability of transitioning from State 0 to State 1 is 0.3, and the probability of staying in State 0 is 0.7. Show more…

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(b) Consider a permanent disability model where = , for all x (i) (ii) Given that = 0.3 and 2 = 0.1, find the probability of transitioning from State 0 to State 1 exactly once and staying in State 1 until time 5.