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Old 05-09-2008, 02:52 AM
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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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Old 05-09-2008, 03:12 AM
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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.
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Old 05-09-2008, 04:21 AM
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(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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Old 05-09-2008, 11:14 AM
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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



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Old 05-09-2008, 01:33 PM
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Quote:
Originally Posted by Jim Daniel View Post
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



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This makes sense. Thanks!
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Old 10-01-2008, 09:10 AM
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Ok, so now I understand how to do this calculation once I have computed the fs', but how were the fs' computed?
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Old 10-01-2008, 09:48 AM
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Just examine how S can eual ech of those values, and then compute the probability for each case.

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Old 10-01-2008, 06:31 PM
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Ok, so fs(2) would be one loss of 2 or 2 losses of 1. Makes sense, thanks!
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Old 09-09-2016, 12:11 AM
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Quote:
Originally Posted by Jim Daniel View Post
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



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Jim, I'm having trouble deciding whether to put condition to the expectation or not. I was able to calculate E(S-3)+ 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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Old 09-09-2016, 02:07 AM
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Jim, I'm having trouble deciding whether to put condition to the expectation or not. I was able to calculate E(S-3)+ 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!
I don't understand why you would even THINK about conditioning on something. Does the expression E[X ^ 3] or E[(X - 3)+] have a "conditioned on" symbol | ? I certainly don't see one. You ask why is it wrong to use conditional expectation. I instead ask where you see anything that indicates that you SHOULD use conditional expectation. E[X ^ 3] simply asks you to compute the average value of the smaller of X and 3. No conditioning, none, nada, niet, nyet, nee.
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