Javier - 1 year ago 360
Python Question

# 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
# 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):
else:
result = "Tails"
return result
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

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):
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()
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])
``````
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