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Math Help - Mean value

  1. #1
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    Mean value

    how to determine E(y) for the joint probability density function fxy(x,y)=2/19 over the range 0<x<5 and 0<y and x-1<y<x+1?

    I tried determining fy for 0<y<1 (fy1) and for 6>y>1 (fy2) separating the space where fxy is defined by the line y=1 and then
    I integrated y*fy1dy from 0 to 6 and then y*fy2dy from 1 to 6 is that a correct method to do it? cause I have:
    fy1=(y+1)*(2/19)
    fy2=(4/19)
    and the result I get is not correct? can anyone see where is my mistake?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Mppl View Post
    how to determine E(y) for the joint probability density function fxy(x,y)=2/19 over the range 0<x<5 and 0<y and x-1<y<x+1?

    I tried determining fy for 0<y<1 (fy1) and for 6>y>1 (fy2) separating the space where fxy is defined by the line y=1 and then
    I integrated y*fy1dy from 0 to 6 and then y*fy2dy from 1 to 6 is that a correct method to do it? cause I have:
    fy1=(y+1)*(2/19)
    fy2=(4/19)
    and the result I get is not correct? can anyone see where is my mistake?
    Draw a picture, then decompose the required integral into pieces that are easy to characterize, You should get something like:

    \displaystyle E(y)=\int_{x=0}^1\int_{y=0}^{x+1}\frac{2}{9}\;y \;dydx +\int_{x=1}^5\int_{y=x-1}^{x+1}\frac{2}{9}\;y \;dydx

    CB
    Last edited by CaptainBlack; January 25th 2011 at 06:16 AM.
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  3. #3
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    It seems to me, and I may be mistaken, that you dont need the third integral. I mean, why didn't you go all the way from 1 to 5 in the second outer integral? And even if you wanted to split the integral why is the iner integral fom x-1 to 5? y is not limited at five I think! well plz clarify me, I would be thankfull
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by Mppl View Post
    It seems to me, and I may be mistaken, that you dont need the third integral. I mean, why didn't you go all the way from 1 to 5 in the second outer integral? And even if you wanted to split the integral why is the iner integral fom x-1 to 5? y is not limited at five I think! well plz clarify me, I would be thankfull
    Yes, you are right I will correct the post.

    CB
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