Probability Density Function Properties
Let f(x) be the probability density function for continuous random variable x. Following are some probability density function properties:
- The probability density function is always positive for all the values of x.
f(x) ≥ 0, ∀ x ∈ R
- The total area under probability density curve is equal to 1.
[Tex]\bold{\int\limits^{\infin}_{-\infin}f(x)dx =1} [/Tex]
- For continuous random variable X, while calculating the random variable probabilities end values of the interval can be ignored i.e., for X lying between interval a and b
P (a ≤ X ≤ b) = P (a ≤ X < b) = P (a < X ≤ b) = P (a < X < b)
- The probability density function of a continuous random variable over a single value is zero.
P(X = a) = P (a ≤ X ≤ a) = [Tex]\bold{\int\limits^{a}_{a}f(x)dx} [/Tex] = 0
- The probability density function defines itself over the domain of the variable and over the range of the continuous values of the variable.
Probability Density Function
Probability Density Function is the function of probability defined for various distributions of variables and is the less common topic in the study of probability throughout the academic journey of students. However, this function is very useful in many areas of real life such as predicting rainfall, financial modelling such as the stock market, income disparity in social sciences, etc.
This article explores the topic of the Probability Density Function in detail including its definition, condition for existence of this function, as well as various examples.
Table of Content
- What is Probability Density Function?
- Probability Density Function Example
- Probability Density Function Formula
- How to Find Probability from Probability Density Function
- Graph for Probability Density Function
- Probability Density Function Properties
- Mean of Probability Density Function
- Median of Probability Density Function
- Variance Probability Density Function
- Standard Deviation of Probability Density Function
- Probability Density Function Vs Cumulative Distribution Function
- Types of Probability Density Function
- Probability Density Function for Uniform Distribution
- Probability Density Function for Binomial Distribution
- Joint Probability Density Function
- Applications of Probability Density Function
- Solved Examples on Probability Density Function