# Section 6: Continuous 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: Section 6 originally covered the Poisson and Exponential Distributions. The Poisson Distribution material was moved to Section 5, and the topics originally in Section 7 were moved into this section after the Exponential Distribution. Sections 8 and later were then renumbered as Sections 7 and later.
Exponential Random Variable

### Examples

Directions: There are no examples for this video.
Exponential 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. Is exponential distribution discrete or continuous? What is its CDF? What is its probability density function? (or probability mass function, whichever is relevant here)?
2. When do we use Exponential distributions?
3. What is the probability of an Exponential random variable $$X$$ with a mean of 3 to be greater than 3?
4. In what sense are exponential and geometric random variables similar?
5. Derive exponential distribution out of a Poisson random variable. What is the conceptual relationship between them? Give an example.
Gaussian Normal 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 is the probability density function of the standard Gaussian random variable?
2. What is the probability density function for the normal random variable $$X$$ with a mean of 2 and variance of 3? What is the probability of $$X>2$$ in terms of $$\Phi$$-values?
3. What is the significance of the normal distribution and when is it used?
Normal Approximation of the Binomial

### 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. State the Central Limit Theorem for Binomial Random variables.
2. When can we approximate Binomial by Normal and how?
Continuity Correction

### 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 the continuity correction and when do we use it?