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Tutorial 3: Question 4

+1 vote
asked Nov 8, 2016 in BUS 3024S - Contingencies by DanNewton (970 points)
recategorized Mar 1 by Rowan

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


1 Answer

+1 vote
answered Nov 9, 2016 by simon_rigby (4,220 points)
selected Nov 15, 2016 by DanNewton
Best answer
Here are some hints:
(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.
Let me know if you need more help, but try to get it on your own!