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# Conditional Distribution

## What is Conditional Distribution?

A probability distribution for a sub-population is known as a Conditional Distribution. Put another way, it shows the likelihood that a randomly selected item in a sub-population has a trait you’re interested in. This is a table with a regular frequency distribution. You can, however, impose conditions on it.
Conditional distributions can also be defined over a set of outcomes for one of the variables.

## Example of Conditional Distribution:

$fX_{1}|X_{2}\left (X_{1}|X_{2}=X_{2} \right )=\frac{fX_{1}X_{2}\left ( X_{1},X_{2} \right )}{f_{X_{1}X_{2}}}$

In other words, it is the joint probability of the two events divided by the marginal probability that X2 = x2.

## Why is conditional distribution important?

Conditional probability is a crucial variable in various fields, including classification, decision theory, prediction, diagnostics, and other comparable scenarios. This is because one person usually makes the classification, judgement, forecast, etc.

Owais Siddiqui