please explain steps

5. Problem. A particle performs a random walk on the integer grid in the plane. It starts at (1,0) and at each step moves one unit up, down, left or right, with probability 1/4 each direction and independently of the previous steps. Thus, at the first step it can move to (0,0),(2,0),(1,1) or (1,1), all with equal probability. There is a square fence with corner posts at (2,2),(2,2),(2,2) and (2,2). The walk stops when the particle 1 hits the fence. Let X be the number of steps of the walk. a) Compute the probability generating function of X. b) Using Part a), find a closed form expression for P(X=n) (no " " " signs). 5. Problem. A particle performs a random walk on the integer grid in the plane. It starts at (1,0) and at each step moves one unit up, down, left or right, with probability 1/4 each direction and independently of the previous steps. Thus, at the first step it can move to (0,0),(2,0),(1,1) or (1,1), all with equal probability. There is a square fence with corner posts at (2,2),(2,2),(2,2) and (2,2). The walk stops when the particle 1 hits the fence. Let X be the number of steps of the walk. a) Compute the probability generating function of X. b) Using Part a), find a closed form expression for P(X=n) (no " " " signs)