In the text below, S means integral and [ ] contain limits [low,high].
Joint PDF: 1=S[0,2]S[0,2](c(x+y)dxdy)⇒
1=cS[0,2]S[0,2]((x+y)dxdy)⇒
1=cS[0,2]((x^2/2+xy)[0,2])dy)⇒
1=cS[0,2](2+2y)dy)⇒
1=c(2y+y^2)[0,2]=8c, c=1/8
f(x,y)=(x+y)/8; P(X=x, Y=y)=(x+y)/8
marginal f[X](x)=(1/8)S((x+y)dy)=(1/8)(xy+y^2/2); applying the range for y: f[X](x)=(2x+2)/8=(x+1)/4
marginal f[Y](y)=(1/8)S((x+y)dx)=(1/8)(x^2/2+xy); applying the range for x: f[Y](y)=(2+2y)/8=(1+y)/4
Conditional densities:
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