A paticle starts at (0,0) and moves in one-unit independed steps with equal probabilites 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, Definde the joint pmf of S and T with n = 3. On a 2D graph, give the probabilities of the joint pmf and the marginal pmfs
b. Let X = S + 3 and Y = T + 3. How are X and Y distributed?