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REMAINDER Group Title

help with the following stat question

  • 2 years ago
  • 2 years ago

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  1. sheg Group Title
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    @remainder??????????????

    • 2 years ago
  2. REMAINDER Group Title
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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

    • 2 years ago
  3. REMAINDER Group Title
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    (2)find E(X) and E(Y)

    • 2 years ago
  4. Zarkon Group Title
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    is the first one \( a/x^2\)

    • 2 years ago
  5. REMAINDER Group Title
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    yes

    • 2 years ago
  6. Zarkon Group Title
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    use \[\sum_{k=1}^{\infty}\frac{1}{k^2}=\frac{\pi^2}{6}\]

    • 2 years ago
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    so it will be \[ a \sum_{1}^{\infty }1/x^{2} =1\] \[a (pi/6)=1\] then a =6/pi

    • 2 years ago
  8. Zarkon Group Title
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    \[a=\frac{6}{\pi^2}\]

    • 2 years ago
  9. REMAINDER Group Title
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    oops i've forgot squared

    • 2 years ago
  10. REMAINDER Group Title
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    then for that one of finding b .how do we do it.

    • 2 years ago
  11. Zarkon Group Title
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    you are really just doing the sum twice so \[\sum_{k=-1}^{-\infty}\frac{1}{k^2}+\sum_{k=1}^{\infty}\frac{1}{k^2}=\frac{\pi^2}{6}+\frac{\pi^2}{6}=\frac{\pi^2}{3}\]

    • 2 years ago
  12. REMAINDER Group Title
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    then b=3/pi^2

    • 2 years ago
  13. Zarkon Group Title
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    yes

    • 2 years ago
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