Question

Code in Python

Problem 1 (2 Points) 1. Write a function randomWalk(.. .) which simulates one path (or trajectory) of a simple symmetric random walk with 2N time steps (i.e. from 0,1,2,...,2N) starting at So-0 nput: lengthofRandomWalk2N Output: samplePath: Array of length 2N+1 with the entire path of the random walk on 0,1,2,..,2N In def randomwalk(lengthofRandomwalk): ## WRITE YOUR OWN CODE HERE # HINT: USE np. random . choice ( ) TO SIMULATE THE INCREMENTS return samplePath In [ ]: ## TEST YOUR FUNCTION HERE print (randomWalk (100)) 2. Plot the trajectory of the random walk you simulated in 1.) In [ ]: WRITE YOUR OWN CODE HERE

Answer 1

import numpy as np
import random
import matplotlib.pyplot as plt

def randomWalk(L):
  
# S is a 2d array where x = row1= S[0][:], y = row2 = S[1][:]
S = np.zeros(shape=(2,L+1))
directions = [1,2,3,4]
for i in range(1, L+1):
direction = np.random.choice(directions)
if direction == 1:
S[0][i] = S[0][i-1] + 1; S[1][i] = S[1][i-1] # go right
elif direction == 2:
S[0][i] = S[0][i-1] - 1; S[1][i] = S[1][i-1] # go left
elif direction == 3:
S[0][i] = S[0][i-1]; S[1][i] = S[1][i-1] + 1 # go up
else:
S[0][i] = S[0][i-1]; S[1][i] = S[1][i-1] - 1; # go down
samplePath = S
return samplePath

n = 100;
path = randomWalk(2*n)

print(path)

x = path[0][:]; y = path[1][:];
plt.figure(1)
plt.plot(x,y,'-')
plt.ylabel('y')
plt.xlabel('x')
plt.show()

import numpy as np import random import matplotlib.pyplot as plt def randomWalk (L) # S is a 2d array where x rowi- S [O] [:], y row2-: S [1] [:] S-np.zeros (shape- (2,L+1)) directions = [1, 2, 3, 4] for i in range (1, L+1): direction np . random . choice (directions) if direction1: # go right St0] [i]S[0] [i-1]+1: S[1] [i]S[1] [i-1] elif direction2: # go left elif direction3: #go up else: # go down samplePath = S return samplePath 100; n path = randomWalk (2n) print (path) x path [0] [ : ] ; y = path plt.figure (l) plt.plot (x, y, '- ') plt.ylabel('y' plt.show ()

65561220331 10212111020 64661311421 00201111021 54752211430 01201120121 55663311321 11201131121 44574321221 1201230130 1 43664232211 01200230231 44665243201 11110130132 34764142301 12100140121 25864142212 12111031121 36754142313 12110122111 36755133313 03200022220 36765034224 12-010-2220 36675034334 01100121221 27575134233 17665034144 02110121211 185650220333010101111020 075661220322011201022120

8 6 4 2 0 2 2 1 0 3 1

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