illustrative abstractions


Continuous Probability Distributions


Aside from the aforementioned Uniform Distribution, there are many types of distributions for continuous random variables.

The Exponential Distribution

Parameter $ \lambda \quad (\lambda > 0) $

The Normal Distribution

Parameter $ \mu, \sigma^2 $

Central Limit Theorem

The sample mean of a large independent random sample (from any distribution) is approximately normally distributed.

$ \bar{X} $ is for large $n$, normal distributed with mean $\mu$ and variance $\frac{\sigma^2}{n}$.

Standard Normal Distribution

Let $ X \sim N(\mu, \sigma^2) $ and let $ Z = \frac{X - \mu}{\sigma} $

$ Z \sim N(0, 1) $ is standard normal distribution.