Probability Between Two Points Calculator
Calculate the probability for a continuous random variable within a specified range using its Probability Density Function (PDF).
Enter the probability density function in terms of x.
The starting point of the interval.
The ending point of the interval.
Understanding Probability Between Two Points
This tool calculates the probability that a continuous random variable falls within a specific interval. To do this, it uses the Probability Density Function (PDF) of the variable.
What is a PDF?
A Probability Density Function (PDF) describes the likelihood of a continuous random variable taking on a given value. For a continuous variable, the probability of it taking any single specific value is zero. Instead, probabilities are calculated over intervals.
How to use this calculator:
- Enter PDF Function: Input the PDF as a mathematical expression in terms of 'x' (e.g.,
x^2,0.5*x,exp(-x)). - Enter Lower and Upper Bounds: Specify the interval [lower bound, upper bound] for which you want to calculate the probability.
- Calculate: Click the 'Calculate Probability' button to get the result. The probability and a visualization of the PDF will be displayed.
The visualization shows the PDF curve, and the shaded area under the curve between the lower and upper bounds represents the calculated probability.
This tool uses numerical integration to approximate the area under the PDF curve, providing an accurate probability calculation.