Continuous Probability Distributions

A continuous probability distribution applies to variables that can take any value within a range - such as height, temperature, or time - rather than only specific, countable values.

Normal (Gaussian) Distribution

The classic bell-shaped curve, symmetric around its mean, where values close to the mean are most likely and extreme values become progressively rarer. Many natural measurements, like human height, approximately follow this distribution.

from scipy.stats import norm

# Probability density at a value, for a normal distribution with mean=170, std=10
density = norm.pdf(180, loc=170, scale=10)
print(density)

# Probability that a value is less than 180
prob = norm.cdf(180, loc=170, scale=10)
print(prob)

Uniform Distribution

Every value within a given range is equally likely - for example, the exact second within a minute at which an event occurs, assuming no bias toward any particular second.

from scipy.stats import uniform

# Probability density for a value between 0 and 10
density = uniform.pdf(5, loc=0, scale=10)
print(density)

Why the Normal Distribution Matters So Much

The Normal distribution shows up constantly in statistics, largely because of the Central Limit Theorem - a concept you'll explore next.

Coming Up Next

Next, you'll learn about the Central Limit Theorem - one of the most important ideas in all of statistics.