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#1




SOA 165
I dont get how E[X ^ 3] is calculated. Some help please?
Is this easy and I'm just burnt out, or am I screwed?
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#2




There's another one later on that is similar. I don't get it either. I didn't see much about in the manual but I am having another look.

#3




(just draw graph of y = 3 and y = x ^ 3)
But , and since for we can compute the expectation as which is one way of seeing that [Conceptually, the only difference between X ^ 3 and 3 occurs when x = 0, 1 or 2 and so you just need to subtract off the right stuff to account for that.]
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#4




It's easy to compute E[S ^ 3] directly. The possible values of S are 0, 1, 2, 3, 4, 5, ... and so the corresponding possible values of S ^ 3 are 0, 1, 2, 3, 3, 3, ... . So
Jim Daniel
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#5




This makes sense. Thanks!
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#6




Ok, so now I understand how to do this calculation once I have computed the fs', but how were the fs' computed?

#7




Just examine how S can eual ech of those values, and then compute the probability for each case.
Jim Daniel
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#8




Ok, so fs(2) would be one loss of 2 or 2 losses of 1. Makes sense, thanks!

#9




Jim, I'm having trouble deciding whether to put condition to the expectation or not. I was able to calculate E(S3)+ but I then divided it by Pr (S>3). Sometimes I can get it right but other times I use the wrong one. So why is it wrong to use the conditional expectation? Thank you!
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#10




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