# Tutorial 3: Question 4

+1 vote
125 views
asked Nov 8, 2016
recategorized Mar 1

I managed a but can't do b or c.

+1 vote
answered Nov 9, 2016 by (4,220 points)
selected Nov 15, 2016

Here are some hints:
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(b) and (c) can both be done as follows. Let $$t$$ denote the time at which payment of a benefit commences. (And the integral w.r.t. $$t$$ will be from $$0$$ to $$\infty$$.)

Then value, as at time $$t$$, the benefit that commences then. This value will be an integral w.r.t. another variable, $$s$$. The integrand you need is the same in the two cases, and involves an occupancy probability. For (b) the integral will be from $$1$$ to $$6$$, for (c) from $$0$$ to $$\infty$$.

So the result is a double integral in both cases.

There may well be other routes in both cases, but this seems simplest.
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Let me know if you need more help, but try to get it on your own!