Suppose that the random variables X and Y have joint p.d.f.f(x,y)=\begin{cases}kx(x-y),0<x<2,-x<y<x\\0,\ \ \ \ elsewhere\end{cases}Find the marginal p.d.f. of the two random variables.

babeeb0oL 2021-05-31 Answered

Suppose that the random variables X and Y have joint p.d.f.
(f(x,y)={kx(xy)0Find the marginal p.d.f. of the two random variables.

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Expert Answer

Demi-Leigh Barrera
Answered 2021-06-01 Author has 97 answers

Given :
(f(x,y)={kx(xy)0
To find marginal P.D.F of x
fx(x)=18xxx(xy)dy
18xx(x2xy)dy
=18[x2yxy22]xx
=18[x3x32+x3+x32]
=18(2x3)
=x34
To find marginal P.D.F of y
fy(y)=1802x(xy)dx
=1802(x2xy)dx
=18[x33x2y2]02
=18[834y200]
=18(83y)
=13y8
=83y24

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