$\DeclareMathOperator{\p}{P}$ $\DeclareMathOperator{\P}{P}$ $\DeclareMathOperator{\c}{^C}$ $\DeclareMathOperator{\or}{ or}$ $\DeclareMathOperator{\and}{ and}$ $\DeclareMathOperator{\var}{Var}$ $\DeclareMathOperator{\Var}{Var}$ $\DeclareMathOperator{\Std}{Std}$ $\DeclareMathOperator{\E}{E}$ $\DeclareMathOperator{\std}{Std}$ $\DeclareMathOperator{\Ber}{Bern}$ $\DeclareMathOperator{\Bin}{Bin}$ $\DeclareMathOperator{\Poi}{Poi}$ $\DeclareMathOperator{\Uni}{Uni}$ $\DeclareMathOperator{\Geo}{Geo}$ $\DeclareMathOperator{\NegBin}{NegBin}$ $\DeclareMathOperator{\Beta}{Beta}$ $\DeclareMathOperator{\Exp}{Exp}$ $\DeclareMathOperator{\N}{N}$ $\DeclareMathOperator{\R}{\mathbb{R}}$ $\DeclareMathOperator*{\argmax}{arg\,max}$ $\newcommand{\d}{\, d}$

Gaussian CDF Calculator


To calculate the Cumulative Density Function (CDF) for a normal (aka Gaussian) random variable at a value $x$, also writen as $F(x)$, you can transform your distribution to the "standard normal" and look up the corresponding value in the standard normal CDF. However, most programming libraries will provide a normal cdf funciton. This tool replicates said functionality.

Calculator

Explanation

This function calculates the cumulative density function of a Normal random variable. It is very important in CS109 to understand the difference between a probability density function (PDF), and a cumulative density function (CDF). The CDF of a random variable at point little $x$ is equal to the probability that the random variable takes on a value less than or equal to $x$. If the random variable is called big $X$, the CDF can be written as $P(X < x)$ or as $F_X(x)$.

The CDF function of a Normal is calculated by translating the random variable to the Standard Normal, and then looking up a value from the precalculated "Phi" function ($\Phi$), which is the cumulative density function of the standard normal. The Standard Normal, often written $Z$, is a Normal with mean 0 and variance 1. Thus, $Z \sim N(\mu = 0, \sigma^2 = 1)$.

Try different calculations to see different translations to the standard normal!