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 November 26th, 2017, 06:24 AM #1 Senior Member   Joined: Jan 2016 From: Blackpool Posts: 104 Thanks: 2 expectation question If E(X)=3, find E(1/x) November 26th, 2017, 10:28 AM #2 Senior Member   Joined: Sep 2015 From: USA Posts: 2,430 Thanks: 1315 what do you think the answer is just by intuition? November 26th, 2017, 01:28 PM   #3
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Quote:
 Originally Posted by Jaket1 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. November 26th, 2017, 02:49 PM #4 Senior Member   Joined: Jan 2016 From: Blackpool Posts: 104 Thanks: 2 so would the answer just be E(1/x)=1/3??? Can you do this though? November 26th, 2017, 02:53 PM   #5
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Quote:
 Originally Posted by Jaket1 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? November 27th, 2017, 02:25 AM #6 Senior Member   Joined: Jan 2016 From: Blackpool Posts: 104 Thanks: 2 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. November 27th, 2017, 01:17 PM #7 Global Moderator   Joined: May 2007 Posts: 6,761 Thanks: 696 You left out the definition of Y in the original problem statement. Tags expectation, question Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Jaket1 Probability and Statistics 4 October 23rd, 2017 10:59 AM eulerrules1 Advanced Statistics 6 December 9th, 2011 09:04 PM hendaz Algebra 2 May 23rd, 2010 01:57 PM hendaz Advanced Statistics 1 May 18th, 2010 01:13 PM nibblebot Advanced Statistics 1 October 30th, 2007 12:05 PM

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