CDF Calculator for Continuous Random Variables

Calculate the Cumulative Distribution Function (CDF) to find the probability that a continuous random variable takes a value less than or equal to a specified value.

Input Parameters

Enter the Probability Density Function (PDF) and the value for which you want to calculate the CDF.

PDF Function (e.g., x^2, exp(-x), 0.5 * exp(-abs(x)))

Value (x)

Calculation Results

CDF Formula:

CDF Value:

Visualization

Understanding CDF for Continuous Random Variables

The Cumulative Distribution Function (CDF), denoted as F(x), for a continuous random variable X gives the probability that X will take a value less than or equal to x. Mathematically, it's defined as:

$$F(x) = P(X \leq x) = \int_{-\infty}^{x} f(t) dt$$

where f(t) is the Probability Density Function (PDF) of the random variable X. The PDF describes the relative likelihood for this random variable to take on a given value.

How to use this tool:

Enter the PDF function in terms of 'x' in the first input box. For example: 0.5 * exp(-abs(x)).
Enter the value of 'x' for which you want to calculate the CDF in the second input box.
Click 'Calculate CDF' to compute the cumulative probability and visualize the PDF and CDF.
Use 'Reset' to clear inputs and outputs.
Copy the calculated CDF value using the 'Copy' button.

This tool uses numerical integration to approximate the CDF value. The visualization helps understand the relationship between the PDF and CDF.