Javier - 6 months ago 56

Python Question

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`

`+1`

`-1`

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`

`-1`

`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`

`+1`

`-1`

`epsilon`

`n`

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`

`import numpy`

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])
```