The joint mass function of a pair of discrete random variables computes probabilities regarding the location of the pair in the plane: . From this it is possible to derive the two marginal mass functions. The first marginal mass function computes probabilities regarding the location of the variable : ; and the second mass function computes probabilities regarding the second variable, : .
Use the locator to move the high probability region (the "bubble" in the picture of the mass function) and watch the effect on the marginal mass functions. Notice that moving the bubble vertically has little effect on the first marginal and moving it horizontally has little effect on the second marginal.