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REMAINDER

  • 3 years ago

help with the following stat question

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  1. sheg
    • 3 years ago
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    @remainder??????????????

  2. REMAINDER
    • 3 years ago
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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

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

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

  5. REMAINDER
    • 3 years ago
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    yes

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

  7. REMAINDER
    • 3 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

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

  9. REMAINDER
    • 3 years ago
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    oops i've forgot squared

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

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

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

  13. Zarkon
    • 3 years ago
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    yes

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