Simulating a coin flip experiment in Python

I am having trouble getting a program to work properly. The goal is to simulate a coin flip as follows:

Consider a random sequence of numbers: epsilon_1, epsilon_2, ... , epsilon_N. Each term in this sequence takes on values +1 or -1, depending on the outcome of the coin toss experiment, heads or tails respectively.

In other words, for each n = 1,2,...,N:

epsilon_n = { +1 with probability = 1/2; and -1 with probability = 1/2.

Now, I wrote some psuedo-code to help me write this program:

# for n = 1,2,...,N:
# flip coin
# if result == "Heads" # epsilon_{n} = 1
# else: # epsilon_{n} = -1

I want to store the values of epsilon for each n (and hence, the result of the experiment for each n) in an array. Here is the program I wrote which hoped to accomplish this:

 # array to store outcome of the coin flip
epsilon = np.zeros(N)
# define coin flip experiment
result = [] # result of the experiment
for n in xrange(1, N): def coin_flip(): #flip coin for each n = 1,...,N flip = random.randint(0,2) if (flip == 0): result = "Heads" else: result = "Tails" return result if result == "Heads": epsilon[n] = 1 else: epsilon[n] = -1
print epsilon

The output of this program is an array with the first entry being 0, and all other entries contain the value -1. I specified N = 100.

Please, some guidance is all I require. For instance, I think I am on the right track with defining a function for the coin toss experiment. I need it to return the result of the experiment (Heads or Tails), and this need to happen for each n = 0,1,...,N but I am unsure of the best method to do so. Then for the result of each individual coin flip, my program must store the value +1 or -1 in the array for epsilon. Must I include n as a parameter for my proposed function?? Am I on the right track here?

Any and all help is very greatly appreciated. Thanks in advance!

EDIT: So I just want to point out I didn't forget to import libraries like numpy and random. Those are included in my original code but this is actually a part of a larger program and so when I copied and pasted this segment of code the import random and import numpy was left out

1 Answer

There are several mistakes in your code. First, you are creating an empty list called result but later in your code result is a string. So you don't need that part.

import numpy as np
import random
N = 10
epsilon = np.zeros(N)

This creates an array of length N for you to store the results. Now, your main error is in the loop. You should define that function outside the loop and call it in each iteration:

def coin_flip(): #flip coin for each n = 1,...,N flip = random.randint(0, 1) if (flip == 0): result = "Heads" else: result = "Tails" return result

Note that I changed the first line to random.randint(0, 1) as it is inclusive on both ends. Now, if you run coin_flip() it will return either "Heads" or "Tails". Change your loop accordingly:

for n in xrange(N): result = coin_flip() if result == "Heads": epsilon[n] = 1 else: epsilon[n] = -1

This is where you are modifying the epsilon array. Note that in each iteration I am calling coin_flip() function and assigning it to result.

Now printing epsilon will give you an array as follows:

array([ 1., 1., 1., -1., -1., 1., -1., -1., -1., -1.])

This is the long way of doing it. Instead, you can do (with random library):

[random.choice([1, -1]) for _ in range(N)]
Out[19]: [1, 1, 1, 1, 1, -1, 1, 1, -1, -1]

Or (with numpy):

np.random.choice([1, -1], N)
Out[20]: array([ 1, 1, 1, 1, -1, -1, -1, -1, -1, -1])