How to Use the Uniform Distribution in Python

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A uniform distribution is a probability distribution in which every value between an interval from a to b is equally likely to be chosen.

The probability that we will obtain a value between x₁ and x₂ on an interval from a to b can be found using the formula:

P(obtain value between x₁ and x₂)  =  (x₂ – x₁) / (b – a)

To calculate probabilities related to the uniform distribution in Python we can use the scipy.stats.uniform() function, which uses the following basic syntax:

scipy.stats.uniform(x, loc, scale)

where:

• x: The value of the uniform distribution
• loc: The minimum possible value
• loc + scale: The maximum possible value

The following examples show how to use this function in practice.

Example 1

Suppose a bus shows up at a bus stop every 20 minutes. If you arrive at the bus stop, what is the probability that the bus will show up in 8 minutes or less?

We can use the following code in Python to calculate this probability:

from scipy.stats import uniform

#calculate uniform probability
uniform.cdf(x=8, loc=0, scale=20) - uniform.cdf(x=0, loc=0, scale=20)

0.4

The probability that the bus shows up in 8 minutes or less is 0.4.

Example 2

The weight of a certain species of frog is uniformly distributed between 15 and 25 grams. If you randomly select a frog, what is the probability that the frog weighs between 17 and 19 grams?

We can use the following code in Python to calculate this probability:

from scipy.stats import uniform

#calculate uniform probability
uniform.cdf(x=19, loc=15, scale=10) - uniform.cdf(x=17, loc=15, scale=10)

0.2

The probability that the frog weighs between 17 and 19 grams is 0.2.

Example 3

The length of an NBA game is uniformly distributed between 120 and 170 minutes. What is the probability that a randomly selected NBA game lasts more than 150 minutes?

We can use the following code in Python to calculate this probability:

from scipy.stats import uniform

#calculate uniform probability 
uniform.cdf(x=170, loc=120, scale=50) - uniform.cdf(x=150, loc=120, scale=50)

0.4

The probability that a randomly selected NBA game lasts more than 150 minutes is 0.4.

Bonus: You can double check the solution to each example by using the Uniform Distribution Calculator.

Additional Resources

The following tutorials explain how to use other common distributions in Python:

How to Use the Binomial Distribution in Python
How to Use the Poisson Distribution in Python
How to Use the t Distribution in Python