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}Evaluate the constant k.

Clifland 2021-05-29 Answered

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

Evaluate the constant k.

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Expert Answer

diskusje5
Answered 2021-05-30 Author has 82 answers

Given :
f(x,y)={kx(xy),0

To find k
f(x,y)dxdy=1
=02xxkx(xy)dxdy=1
=02xxk(x2xy)dydx=1
=02k[x2yxy22]xxdx=1
=02k[x3x32+x3+x32]dx=1
=02k[2x3]dx=1
=2k[x44]02=1
=2k(4)=1
=k=18

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