Normal Distribution

What is a Normal Distribution?

The Normal Distribution is probably the most important and commonly-encountered probability distribution. Height in humans, for example, is normally distributed. Though many distributions are bell-shaped, a normal distribution is often considered THE “bell curve”. It's also the distribution off of which our ideas of standard deviation are based.

Normal distribution, despite its simple name and relatively easy-to-understand definition, is actually a very interesting concept. Any time you add together a large amount of random variables, even if those variables are from different distributions, if you get enough samples you'll find that the sum of the variables tends to be normally distributed. 

It's also called the Gaussian distribution named after Johann Carl Friedrich Gauss, the man credited with the introduction of the distribution to mathematics.

Applications in Machine Learning and AI 

In machine learning, it’s normal to have different errors from many different sources, from data corruption to classification errors. While it’s important to always check to ensure your assumption is correct, it’s not unreasonable to think that the combined effect of these errors is approximately normal. Accepting the normal distribution also makes the math easier and faster to do, which is an important consideration when teaching AI. Due to the simplicity of normal distribution, it is almost always an excellent place to start, even if it isn’t the distribution one uses in the end.