 # Section 7: Joint Distribution Function, Marginal Probability Mass Function, and Uniform Distribution

### Instructions

• This section covers the concepts listed below.
• For each concept, there is a conceptual video explaining it followed by videos working through examples.
• When you have finished the material below, you can go to the next section or return to the main Mathematical Probability page

### Concepts

Joint Distribution and Joint PMF

### Examples

Directions: There are no examples for this video.
Marginal PMF

### Examples

Directions: There are no examples for this video.
Joint PMF of Continuous Random Variables

### Examples

Directions: There are no examples for this video.
Joint PDF

### Examples

Directions: The following examples cover the material from the video above.
Joint PMF and Marginal PMF

### Examples

Directions: The following examples cover the material from the video above.

### Self-Assessment Questions

Directions: The following questions are an assessment of your understanding of the material above. If you are not sure of the answers, you may need to rewatch the videos.

Note: These self-assessment questions apply to all the videos listed above on this page.
1. What does a joint distribution mean? How is it related to vector-valued random variables?
2. Define the joint probability mass function of two discrete random variables.
3. Can we find the joint distribution of two random variables knowing their individual distribution? What about the converse question? Consider both discrete and continuous cases.
Uniform Distribution

### Examples

Directions: The following examples cover the material from the video above.

### Self-Assessment Questions

Directions: The following questions are an assessment of your understanding of the material above. If you are not sure of the answers, you may need to rewatch the videos.
1. How do you find the marginal distributions of the coordinates of a point randomly selected inside a solid of finite volume?