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Thread: Are the random variables X and Y independent or not?

  1. #1
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    Are the random variables X and Y independent or not?

    Hey, I'm stuck with step b):

    Are the random variables X and Y independent or not?-img_9928.png

    I know that i will get c by integrating
    ∫f(x,y)dxdy=1but how do i know if x and y are independent or not?


    thank you for your help!



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  2. #2
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    Re: Are the random variables X and Y independent or not?

    When you have done part a) and determined the distribution for $\displaystyle X$ and $\displaystyle Y$ you can use the fact that $\displaystyle X$ and $\displaystyle Y$ are independent iff.

    $\displaystyle F_{X,Y}(x,y) = F_X(x)F_Y(y)$ or $\displaystyle f_{X,Y}(x,y) = f_X(x)f_Y(y)$

    Where $\displaystyle f_{X,Y}$ are the joint p.d.f of $\displaystyle X$ and $\displaystyle Y$ and $\displaystyle F_{X,Y}$ are the respective the c.d.f
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