## What is Conditional Probability Density Function (Conditional PDF)?

A probability density function is known as conditional PDF, when one random variable out of two random variables has a fixed value. Here suppose we have two random variables X and Y, and X has a fixed value equal to x.
In this case in the conditional PDF of Y when X=x is given as-

In the same way, Conditional PDF of X when random variable Y takes a fixed value Y=y is given as-

## Properties of Conditional Probability Density Function (Conditional PDF)

Property 1- Conditional PDF is a non-negative function.

As conditional PDF is a ratio of two PDFs and we know that PDF is a non-negative function. Therefore the ratio of two non-negative PDFs is also non- negative function.

Property 2- Area under the conditional PDF is unity i.e. one.
This property mathematically can be expressed as-

Probability Density Function (PDF) - Definition, Basics and Properties of Probability Density Function (PDF) with Derivation and Proof

Property 3- Conditional probability density function (conditional PDF) reduces to marginal density if random variables X and Y are statistically independent.

1. 