Normal Distribution

The normal (or Gaussian) distribution is a common probability distribution.

Equation

The distribution's probability density function is

$$f(x) = \frac{1}{\sigma\sqrt{2\pi}}e^{\frac{-(x-\mu)^2}{2\sigma^2}}$$

This equation has two parameters: $$\mu$$ and $$\sigma$$. $$\mu$$ is the mean of the distribution. $$\sigma$$ is the standard deviation. The normal distribution is often just represented by these two parameters.

Properties

• Bell-shaped curve.
• Total area under the curve is 1.
• Symmetrical

Standard Normal Distribution

The standard normal distribution is simply when $$\mu$$ = 0, $$\sigma$$ = 0.