Wrong input distributions

You'll continue working with the pi example in this exercise: A graph of a circle inside a square with randomly sampled points

What happens if you change the input probability distribution from the continuous uniform distribution(random.uniform()) to the discrete uniform distribution(random.randint())? Your results will not be reliable, because random.randint() will sample discrete integers, while random.uniform() samples continuous float numbers.

Pay attention to the estimated pi value that this simulation generates. Because the incorrect probability distribution has been selected, it will not be very accurate! Choosing the correct probability distributions is essential for Monte Carlo simulations, and we will go into more detail on different distributions in later lessons so that you feel confident you are choosing the correct one going forward.

random has been imported for you.

This exercise is part of the course

Monte Carlo Simulations in Python

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Exercise instructions

Sample the x and y coordinates in the interval from -1 to 1 using random.randint() rather than the correct random.uniform() function used in the video.

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

n = 10000
circle_points = 0 
square_points = 0 
for i in range(n):
    # Sample the x and y coordinates from -1 to 1 using random.randint()
    x = ____
    y = ____
    dist_from_origin = x**2 + y**2
    if dist_from_origin <= 1:
        circle_points += 1
    square_points += 1
pi = 4 * circle_points / square_points
print(pi)

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