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Conditional expectations

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asked Nov 9 in BUS 3024S - Contingencies by Rohin

BUS3024S Test 1 2006.pdf (0,1 MB)

In the above paper, for Question 5, the memo uses the following statement. 

$$E[v^{K_{60}+1}|K_{60}\ge 10]=E[V^{K_{70}+11}]$$

I was under the belief that we are only allowed to drop the conditional part of an expectation if the random variables were independent. i.e. \(K_{60}\) and \(K_{70}\) were independent. However, surely \(K_{60}\) and \(K_{70}\) are not independent?  

1 Answer

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answered Nov 14 by Emiel_Zyde (720 points)
You are not really dropping the conditional expectation. You should think of it as a re-parametrization. Given that the curtate future lifetime of the life aged 60 is greater than or equal to 10, we are just reparametrizing the life to be aged 70.