Question

help with the following stat question

Answer 1

@remainder??????????????

Answer 2

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

Answer 3

(2)find E(X) and E(Y)

Answer 4

is the first one \( a/x^2\)

Answer 5

yes

Answer 6

use \[\sum_{k=1}^{\infty}\frac{1}{k^2}=\frac{\pi^2}{6}\]

Answer 7

so it will be

\[ a \sum_{1}^{\infty }1/x^{2} =1\]
\[a (pi/6)=1\]
then a =6/pi

Answer 8

\[a=\frac{6}{\pi^2}\]

Answer 9

oops i've forgot squared

Answer 10

then for that one of finding b .how do we do it.

Answer 11

you are really just doing the sum twice so

\[\sum_{k=-1}^{-\infty}\frac{1}{k^2}+\sum_{k=1}^{\infty}\frac{1}{k^2}=\frac{\pi^2}{6}+\frac{\pi^2}{6}=\frac{\pi^2}{3}\]

Answer 12

then b=3/pi^2

Answer 13

yes