Joint and marginal distribution functions. For any two random variables X and Y defined on the same sample space, the joint c.d.f. is For an example, see next slide. The marginal distributions can be obtained from the joint distributions as follows:
Y=0 Y=3 Y=4
X=5 1/7 1/7 1/7 3/7
X=8 3/7 0 1/7 4/7
4/7 1/7 2/7
The right-hand-side of the latter equation defines the convolution of fX and fY.