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__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. __What is Conditional Probability Density Function (Conditional PDF)?__

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-

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

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

**- Conditional PDF is a non-negative function.**

__Property 1__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.

__- Area under the conditional PDF is unity i.e. one.__

**Property 2**This property mathematically can be expressed as-

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__READ THIS ALSO__:-**Probability Density Function (PDF) - Definition, Basics and Properties of Probability Density Function (PDF) with Derivation and Proof**

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

__Property 3__**Go to HOME Page**

__Read More-__**Random Variables (Discrete and Continuous Random Variables), Sample space and Random Variables Examples**

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

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