Use python

We will write code to describe the random$-$walk of an ant which starts at the origin. At each time step the ant jumps either to the left or the right. Let's assume that the jump can therefore be any number in the range $[1,1)($so the jumps can be different sizes, in addition to different directions$).$ Consider the situation where the ant makes a total of $100$ jumps.

a$)$ In the cell below, write a program to run $500$ experiments of this random walk. For each of the experiments, you need to save the final position in an array, for example, dist.

Plot a histogram of the final positions that the ant reaches: plt$.$hist$($dist$,$number of bins$).$ Remember to label your axes.

b$)$ The distance from the starting point $($the origin$)$ can be found using the np$.$abs function, which returns the absolute value of a quantity. Write code that plots the histogram of the absolute values of your final position in the previous part.

c$)$ Transform your code in part a$)$ into a function that takes as input the number of experiments $($Ne$)$ and the number of steps $($Ns$).$ Name your function ant$\_$walk$()$ and return the average distance travelled by the ant. To calculate the average distance you can use np$.$mean$($dist$)$

d$)$ Using a for loop, call your function, each time changing the number of steps,

but keeping the number of experiments equal to $500.$ As steps use $50,100,150,$

$200,...,2000.$

Plot the average distance moved as a function of the number of steps

$($ plt$.$plot $(x,y)$

Hint: You can create a list of steps and loop over the list. An example is given:

for s in steps:

print$($s$)$

The index $s$ will step through the values in the list steps. You can pass this

index to your function. To save the value of the mean, you can create an empty list

and append the mean value to it using $.$append$()$

L $=[]$

for $s$ in steps:

L$.$ append $($s$)$

This code just copies all the values of steps into the list $L.$

# Write code here

e$)$ Use the NumPy function power $()$ to plot different integer powers of $L$ versus

steps. See if you can identify the power which yields a straight line plot, i$.$e$.$

plot $L^n$ versus $n$ for a choice of $n$ which makes $L^n$ close to a straight

line. Before you explore this, you might like to generate 'good' values of $L$ by

running your code in the previous cell for $10000$ experiments for each step value.