A particle starts at 0 0 and moves in oneunit independent st

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 T with n = 3. On a two–dimensional graph, give the probabilities of the joint pmf and the marginal pmfs.

(b) What are the marginal distributions of X and Y?

Solution