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Science Forum Index » Statistics - Math Forum » Variance of two random variables
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Message |
| fl |
 Posted: Tue Jan 02, 2007 11:22 pm |
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Guest
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Hi,
I want to get the variance of a series variables in my project. The
possiblity of vriable random1 is P, the possibility of random2 is 1-P.
The variances Var1 and Var2 are known for random1 and random2
respectively. I want to know the ensemble variance of the stream
random1 and random2. I have not verified it is P*Var1+(1-P)*Var2 in
mathmatics. Could you help me? Thank you very much. |
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| David Jones |
| Posted: Wed Jan 03, 2007 6:17 am |
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Guest
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fl wrote:
Quote: Hi,
I want to get the variance of a series variables in my project. The
possiblity of vriable random1 is P, the possibility of random2 is
1-P.
The variances Var1 and Var2 are known for random1 and random2
respectively. I want to know the ensemble variance of the stream
random1 and random2. I have not verified it is P*Var1+(1-P)*Var2 in
mathmatics.
Just as well, since it is not correct except in a special case (which
just might apply to your problem).
Quote: Could you help me? Thank you very much.
(i) recall the defintitions of E(X) and E(X^2);
(ii) recall the formula expressing var(X) in terms of E(X^2) and E(X);
(iii) for your mixture model:
(a) ensure you know/believe the (probably inbuilt) assumption of
independence between the various random items here (including
statistical independence between the value of the selected variable,
once selected, and the process selecting it);
(b) work out formulae for E(X^2) and E(X) in terms of the
underlying quantities;
(iv) get the formula for var(X) by combining (iii) and (ii).
David Jones |
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