 # Section 5: Discrete Distributions

### 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
• Note: the last four items concerning the Poisson Random Variable were originally in Section 6.
Binomial Random Variable

### Examples

Directions: There are no examples for this video.

### 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. Define Bernoulli and binomial distributions. What is the relation between them from a conceptual point of view?
2. What are the expectation and variance of a binomial random variable.
Indicator Random Variable

### Examples

Directions: There are no examples for this video.

### 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. Define an indicator random variable for one of your favorite events in the experience of rolling a fair die. How many indicator random variables can be defined for that experience?
Geometric Random Variable

### Examples

Directions: There are no examples for this video.

### 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. Why do we call it a geometric random variable? Does it have any connections to the geometric series in calculus?
2. What does a geometric distribution describe?
3. Estimate the expected value and variance of a geometric distribution if success in each of the underlying Bernoulli trials is: almost certain, almost impossible, equally likely as failure.

Pascal Random Variable

### 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 does the Pascal distribution model?
Negative Binomial Random Variable

### 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 does a negative binomial distribution model?
2. What is the relation between Pascal, Negative Binomial, and Geometric distributions?
Poisson Random Variable Conceptual

### Examples

Directions: There are no examples for this video.

### 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 the probability mass function of a Poisson RV?
2. Give some examples of random variables that follow Poisson distribution in time. How about an example in Space?
3. What is the probability mass function of a Poisson random variable whose mean equals to 2?
Law of Rare Events

### Examples

Directions: There are no examples for this video.

### 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 the significance of Poisson distributions? Express the Law of Rare Events?
Approximating Binomial Distribution from Poisson

### Examples

Directions: There are no examples for this video.

### 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. When can we approximate Binomial by Poisson?
Poisson Random Variable and Law of Rare Events

### Examples

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