anonymous
  • anonymous
help with the following stat question
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
@remainder??????????????
anonymous
  • anonymous
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
anonymous
  • anonymous
(2)find E(X) and E(Y)

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Zarkon
  • Zarkon
is the first one \( a/x^2\)
anonymous
  • anonymous
yes
Zarkon
  • Zarkon
use \[\sum_{k=1}^{\infty}\frac{1}{k^2}=\frac{\pi^2}{6}\]
anonymous
  • anonymous
so it will be \[ a \sum_{1}^{\infty }1/x^{2} =1\] \[a (pi/6)=1\] then a =6/pi
Zarkon
  • Zarkon
\[a=\frac{6}{\pi^2}\]
anonymous
  • anonymous
oops i've forgot squared
anonymous
  • anonymous
then for that one of finding b .how do we do it.
Zarkon
  • Zarkon
you are really just doing the sum twice so \[\sum_{k=-1}^{-\infty}\frac{1}{k^2}+\sum_{k=1}^{\infty}\frac{1}{k^2}=\frac{\pi^2}{6}+\frac{\pi^2}{6}=\frac{\pi^2}{3}\]
anonymous
  • anonymous
then b=3/pi^2
Zarkon
  • Zarkon
yes

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