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help with the following stat question
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sheg
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@remainder??????????????
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let X have mass function\[ f_{x}(x)=(a/)x^{2} ;x=1,2,..... \] and Y have mass function \[ f_{y}(y) =(b/y^{2} ) y =\pm1,\pm2\] find a and b
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(2)find E(X) and E(Y)
Zarkon
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is the first one \( a/x^2\)
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yes
Zarkon
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use \[\sum_{k=1}^{\infty}\frac{1}{k^2}=\frac{\pi^2}{6}\]
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so it will be
\[ a \sum_{1}^{\infty }1/x^{2} =1\]
\[a (pi/6)=1\]
then a =6/pi
Zarkon
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\[a=\frac{6}{\pi^2}\]
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oops i've forgot squared
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then for that one of finding b .how do we do it.
Zarkon
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you are really just doing the sum twice so
\[\sum_{k=-1}^{-\infty}\frac{1}{k^2}+\sum_{k=1}^{\infty}\frac{1}{k^2}=\frac{\pi^2}{6}+\frac{\pi^2}{6}=\frac{\pi^2}{3}\]
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then b=3/pi^2
Zarkon
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yes