A particle starts at (0, 0) and moves in one-unit independent steps with equal probabilities of 1/4 in each of the four directions: north, south, east, and west. Let S equal the east-west position and T the north-south position after n steps. (a) Define the joint pmf of S and Twith n 3. On a two-dimensional graph, give the probabilities of the joint pmf and the marginal pmfs (similar to Figure 4.1-1) (b) What are the marginal distributions of X and Y?