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Probability Density Formula:
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Probability density describes the relative likelihood for a continuous random variable to take on a given value. It represents the probability per unit length along the x-axis in probability distributions.
The calculator uses the probability density formula:
Where:
Explanation: This formula calculates how much probability is distributed per unit of measurement in a continuous probability distribution.
Details: Probability density functions are fundamental in statistics and probability theory. They help describe continuous random variables, calculate probabilities over intervals, and understand the distribution of data in fields such as physics, engineering, and finance.
Tips: Enter the probability value as a decimal between 0 and 1, and the interval width as a positive number. The calculator will compute the probability density per unit.
Q1: What's the difference between probability and probability density?
A: Probability measures the likelihood of an event (0 to 1), while probability density measures how probability is distributed per unit in continuous distributions.
Q2: Can probability density be greater than 1?
A: Yes, probability density can be greater than 1. Unlike probabilities, density values aren't bounded between 0 and 1 because they represent probability per unit.
Q3: What are common applications of probability density?
A: Used in statistical modeling, risk assessment, physics (quantum mechanics), engineering (signal processing), and finance (option pricing).
Q4: How does interval width affect probability density?
A: For a fixed probability, a smaller interval width results in higher density, while a larger interval width results in lower density.
Q5: What's the relationship between PDF and CDF?
A: The probability density function (PDF) is the derivative of the cumulative distribution function (CDF). The CDF gives the probability that a random variable is less than or equal to a certain value.