# Section 9: Conditional Distribution and Conditional Expectation

### 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

Conditional 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. What is a conditional probability mass function?
Conditional Expectation

### 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. What is conditional expectation?
2. How do you define the conditional probability mass function $$X$$ given $$Y=y$$ in the discrete case? What about the corresponding conditional expectation?
3. How do you define the conditional probability density function of $$X$$ given $$Y=y$$ in the continuous case?
Conditional Density Function

### Examples

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