  # Conditional Probability Distribution

## What is Conditional Probability Distribution?

Conditional probability distribution is the likelihood of one condition being true if another condition is known to be true. This forms the foundation of Bayes’ theorem and Bayesian networks

In machine learning notation, the conditional probability distribution of Y given X is the probability distribution of Y if X is known to be a particular value or a proven function of another parameter. Both can also be categorical variables, in which case a probability table is used to show distribution.

This is not to be confused with the marginal distribution of a random variable, which is a distribution without a relationship to the value of the other variable.

Conditional probability also differs from joint probability, which is the probability that both conditions are true without knowing that any of them are true.

### Where are Conditional Probability Distributions Used?

• Calculating Discrete distributions in Bayes' Theorem
• Calculating Continuous distributions
• Calculating Measure-theoretic formulations
• Forming Conditional expectations