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November 26th, 2017, 06:24 AM   #1
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expectation question

If E(X)=3, find E(1/x)
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November 26th, 2017, 10:28 AM   #2
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what do you think the answer is just by intuition?
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November 26th, 2017, 01:28 PM   #3
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Quote:
Originally Posted by Jaket1 View Post
If E(X)=3, find E(1/x)
I depends entirely on the distribution of X. 2 Examples.
1. P(X=3)=1: E(1/X)=1/3
2. P(X=0)=1/2, P(X=6)=1/2: E(1/X) is infinite.
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November 26th, 2017, 02:49 PM   #4
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so would the answer just be E(1/x)=1/3??? Can you do this though?
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November 26th, 2017, 02:53 PM   #5
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Quote:
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so would the answer just be E(1/x)=1/3??? Can you do this though?
no, in general as Mathman has pointed out, you can't.

It's a strange question as without more information about the density you can't give any definite answer.

Is there more information about the density?
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November 27th, 2017, 02:25 AM   #6
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Hi Romsek, the actual question is:
X~Gam(3,1) and (y|X=x)~Exp(x)

Find E(Y)

This is what I have done and also the reason I asked the first question:

we know that E(X)=1/x for an exp(x) distribution and hence E(Y|X=x)=1/x and therefore E(Y)=E(E(Y|X)=E(1/x)

we also know that E(X) of a gamma distribution is E(X)=$\frac{\alpha}{\beta}$ where gam~($\alpha,\beta$)

hence E(X)=3 and this is where i got stuck.

Perhaps I have made a mistake somewhere.
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November 27th, 2017, 01:17 PM   #7
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You left out the definition of Y in the original problem statement.
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