Cumulative Probability Function and the Central Limit Theorem

Learn about cumulative probability, the Gaussian error function, central limit theorem, and how to measure the difference between distributions.

We'll cover the following

Gaussian error function and cumulative probability (density) function
Functions of random variables and the central limit theorem
Measuring the difference between distributions

Gaussian error function and cumulative probability (density) function

We have mainly discussed probabilities of single values as specified by the probability (density) functions. However, in many cases, we need to know the probabilities of having values within a certain range. The probability of a specific value of a continuous random variable is actually infinitesimally small (nearly zero), and only the probability of a range of values is finite and has a useful meaning of a probability. This integrated version of a probability density function is the probability of having a value $x$ for the random variable $X$ in the range of $x_1 \leq x \leq x_2$ and is given by the following equation:

Get hands-on with 1400+ tech skills courses.

Getting started

Introduction

Scientific Programming with Python

Machine Learning with Sklearn

Neural Networks and Keras

Regression and Optimization

Basic Probability Theory

Probabilistic Regression and Bayes Nets

Generative Models

Cyclic Models and Recurrent Neural Networks

Reinforcement Learning

Artificial intelligence, the Brain, and Our Society

Conclusion

Cumulative Probability Function and the Central Limit Theorem

Gaussian error function and cumulative probability (density) function