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REMAINDER
 3 years ago
help with the following stat question
REMAINDER
 3 years ago
help with the following stat question

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REMAINDER
 3 years ago
Best ResponseYou've already chosen the best response.1let 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

REMAINDER
 3 years ago
Best ResponseYou've already chosen the best response.1(2)find E(X) and E(Y)

Zarkon
 3 years ago
Best ResponseYou've already chosen the best response.1is the first one \( a/x^2\)

Zarkon
 3 years ago
Best ResponseYou've already chosen the best response.1use \[\sum_{k=1}^{\infty}\frac{1}{k^2}=\frac{\pi^2}{6}\]

REMAINDER
 3 years ago
Best ResponseYou've already chosen the best response.1so it will be \[ a \sum_{1}^{\infty }1/x^{2} =1\] \[a (pi/6)=1\] then a =6/pi

REMAINDER
 3 years ago
Best ResponseYou've already chosen the best response.1oops i've forgot squared

REMAINDER
 3 years ago
Best ResponseYou've already chosen the best response.1then for that one of finding b .how do we do it.

Zarkon
 3 years ago
Best ResponseYou've already chosen the best response.1you 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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