## anonymous 4 years ago help with the following stat question

1. anonymous

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

2. 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

3. anonymous

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

4. Zarkon

is the first one $$a/x^2$$

5. anonymous

yes

6. Zarkon

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

7. anonymous

so it will be $a \sum_{1}^{\infty }1/x^{2} =1$ $a (pi/6)=1$ then a =6/pi

8. Zarkon

$a=\frac{6}{\pi^2}$

9. anonymous

oops i've forgot squared

10. anonymous

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

11. Zarkon

you are really just doing the sum twice so $\sum_{k=-1}^{-\infty}\frac{1}{k^2}+\sum_{k=1}^{\infty}\frac{1}{k^2}=\frac{\pi^2}{6}+\frac{\pi^2}{6}=\frac{\pi^2}{3}$

12. anonymous

then b=3/pi^2

13. Zarkon

yes

Find more explanations on OpenStudy