Marginal Probability Density Function (Marginal PDF) - Marginal Densities with Derivation and Proof

What is Marginal Probability Density Function (Marginal PDF) or Marginal Densities?

When the PDFs fx(x) and fy(y) for any single random variable are obtained from the joint PDF, in that case fx(x) and fy(y) are called as marginal PDF or marginal densities.

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 Proof-

Now to find the CDF of random variable X, the value of other random variable Y, does not matter.

Similarly we can get-

Here fx(x) and fy(y) are known as marginal PDF or simply marginal densities as both of these PDFs are obtained from the joint PDF.

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