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__What is Joint Probability Density Function or Joint PDF__?

Joint PDF is simply the PDF of two or more random variables.The joint probability density function of any two random variables X and Y can be defined as the partial derivative of the joint cumulative distribution function, with respect to dummy variables x and y.

Mathematically-

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__Watch the Complete Video Here__

__Watch the Complete Video Here__

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

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__Joint PDF Formula__

__Joint PDF Formula__

Joint PDF Formula |

Now we will discuss the properties of joint probability density function (joint PDF)

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__Properties of Joint Probability Density Function (Joint PDF)__

__Properties of Joint Probability Density Function (Joint PDF)__

**- Joint PDF is non-negative.**

__Property 1__Joint PDF Property |

Since joint PDF is a derivative of joint cumulative distribution function (Joint CDF), which is also a non negative function.

Therefore joint PDF is always positive.

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__READ THIS ALSO__:-**Cumulative Distribution Function (CDF) - Properties of CDF - CDF Definition, Basics - Continuous and Discrete CDF**

**- The joint PDF is continuous everywhere as the joint CDF is continuous and we know that it is the derivative of joint CDF.**

__Property 2__**- The total volume under the surface of joint PDF is equal to Unity.**

__Property 3__Joint PDF Property |

Now we will discuss an important property of two statistically independent random variables X and Y.

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__Statistically Independent Random Variables X and Y__

For two statistically independent random variables X and Y-__Statistically Independent Random Variables X and Y__

Statistically independent random variables X and Y |

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__READ THIS ALSO__:-**Joint Cumulative Distribution Function - Joint Distribution Function - Combined CDF**

Proof-

Statistically Independent Random Variables X and Y |

__Relation between Probability and Joint PDF__

__Relation between Probability and Joint PDF__

Relation between Probability and Joint PDF |

On extending this relation to two random variables X and Y-

Relation between Probability and Joint PDF for two Random Variables |

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__READ THIS ALSO__:-**Conditional Probability Density Function (Conditional PDF) - Properties of Conditional PDF with Derivation**

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__Relationship between joint PDF and Probability for statistically independent random variables X and Y__

__Relationship between joint PDF and Probability for statistically independent random variables X and Y__

If two random variables X and Y are statistically independent, then the joint PDF of X and Y is given as the product of two separate PDFs.

Relationship between joint PDF and Probability for statistically independent random variables X and Y |

Relationship between joint PDF and Probability for statistically independent random variables X and Y |

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