Part 1 - Random Walks - 9 marks Suppose we have a 2D lattice of size 100 x 100 u
ID: 2966365 • Letter: P
Question
Part 1 - Random Walks - 9 marks
Suppose we have a 2D lattice of size 100 x 100 units, and we position a walker at a
starting point (x0; y0). You are to simulate a random walk on the lattice, taking steps
of length 1 unit with
Case 1: a choice of 4 directions described by the compass points N, E, S and W;
Case 2: a choice of 8 directions N, NE, E, SE, S, SW, W and NW.
In each case, the choice of direction is uniformly distributed. You should consider the
lattice as having a wrap-around property, i.e. if the walker steps off the lattice at the
top (or bottom), s/he appears in the same column at the bottom (or top) of the lattice;
similarly for stepping off one of the sides, with the walker appearing in the same row on
the opposite side.
You are to carry out a random walk with M steps in each path, and calculate the total
displacement at the end of the walk sqrt
(xM - x0)2 + (yM -y0)^2. Simulate N such paths,and compute the average displacement.
Your code should be in MATLAB, and should accept input parameters M and N, as well
as a flag indicating the choice of 4 or 8 directions. You should plot a figure in MATLAB
showing the average displacement versus M, for M = 49; 64; 100; 144 steps for each of
Cases 1 and 2.
You should also write a paragraph, where you discuss your answer interpreting the
average displacement result and also justifying your choice of the value of N that you
use.
Part 2 - Sampling from Experimental Data - 6 marks
The data file inputData60.txt contains 60 samples of data from some experiments. In
MATLAB, construct the distribution function F(x) for this data and generate 300 ran-
dom variables from this distribution. Plot both the histogram of the experimental data
and your generated data, to confirm that they seem to belong to the same probability
distribution.
inputData60.txt
0.2969
0.4242
0.4445
0.0891
0.1390
0.0782
0.3479
0.6249
0.6616
0.1152
0.2660
0.2118
0.7137
0.1306
0.7318
0.7015
0.7226
0.1407
0.6894
0.1883
0.5507
0.2377
0.2812
0.7232
0.6528
0.4864
0.0835
0.1478
0.3133
0.6707
0.2609
0.2245
0.4043
0.1014
0.5780
0.5932
0.4653
0.3303
0.6138
0.1998
0.6870
0.1774
0.1670
0.3629
0.1572
0.5077
0.5292
0.3850
0.2516
0.7298
0.1081
0.6338
0.7094
0.4486
0.1227
0.5720
0.7294
0.3661
0.5198
0.0951