Questions: The uniform, normal, and exponential distributions are all continuous probability distributions. are all discrete probability distributions. can be either continuous or discrete, depending on the data. are all the same distributions.

The uniform, normal, and exponential distributions are all continuous probability distributions. are all discrete probability distributions. can be either continuous or discrete, depending on the data. are all the same distributions.

Transcript text: The uniform, normal, and exponential distributions are all continuous probability distributions. are all discrete probability distributions. can be either continuous or discrete, depending on the data. are all the same distributions.

Solution

Solution Steps

To determine the nature of the uniform, normal, and exponential distributions, we need to understand the definitions and properties of these distributions. The uniform, normal, and exponential distributions are all continuous probability distributions.

Step 1: Identify the Distributions

The uniform, normal, and exponential distributions are all types of probability distributions. We need to classify each of them based on their characteristics.

Step 2: Classify Each Distribution

The uniform distribution is defined such that all outcomes are equally likely within a specified range. It is a continuous distribution.
The normal distribution is characterized by its bell-shaped curve and is defined by its mean \( \mu \) and standard deviation \( \sigma \). It is also a continuous distribution.
The exponential distribution is often used to model the time until an event occurs and is defined by its rate parameter \( \lambda \). This distribution is continuous as well.

Step 3: Conclusion

Since all three distributions (uniform, normal, and exponential) are classified as continuous probability distributions, we conclude that the statement regarding their nature is correct.