Probability Density Function (PDF) Calculator

Visualize and calculate the Probability Density Function for continuous random variables.

Input Parameters

Define the range for the random variable and the probability density function.

Range (min, max):

PDF Function f(x):

Result

PDF Value at midpoint:

PDF Visualization

Understanding Probability Density Function (PDF)

The Probability Density Function (PDF) is used for continuous random variables. Unlike probability mass functions for discrete variables, the PDF doesn't give the probability of a specific value but rather the probability density at that value. The area under the PDF curve over a range gives the probability that the random variable falls within that range. For example, the standard normal distribution's PDF is often visualized as a bell curve. This tool helps you explore and visualize PDFs for different functions you input.

Formula Example: For a normal distribution, the PDF is given by: $$ f(x) = \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{1}{2}(\frac{x-\mu}{\sigma})^2} $$ where $ \mu $ is the mean and $ \sigma $ is the standard deviation.

Use this calculator to input your function and range to see its PDF and calculate density at the midpoint.