Definition: A joint probability distribution describes the probability of multiple events occurring together.

Detailed Description:

In probability theory, a joint probability distribution specifies the probability of two or more random variables taking on specific values simultaneously. It is often represented as a joint probability mass function or joint probability density function.

Joint probability distributions are used to model relationships between variables and to calculate conditional probabilities.

Related Terms:

• Probability
• Random Variable
• Marginal Probability
• Conditional Probability
• Independence

FAQs:

1. What is the difference between a joint probability distribution and a marginal probability distribution?

   • A joint probability distribution describes the probability of multiple events occurring together, while a marginal probability distribution describes the probability of a single event occurring.  
     
      

2. How is conditional probability related to joint probability?

   • Conditional probability is calculated using the joint probability distribution and the marginal probability distribution.

3. What are some applications of joint probability distributions?

   • Joint probability distributions are used in various fields, including statistics, machine learning, and finance.