A random variable with an equally likely chance of assuming any value within a specified range is said to have a continuous uniform distribution.

Here's the reasoning:

• Binomial distribution: This is a discrete distribution that represents the number of successes in a fixed number of independent Bernoulli trials, each with the same probability of success.

• Geometric distribution: This is a discrete distribution that represents the number of trials needed to get the first success in a sequence of independent Bernoulli trials, each with the same probability of success.

• Discrete uniform distribution: This is a distribution where each of a finite number of values is equally likely. It is not applicable to continuous ranges.

• Continuous uniform distribution: This is a distribution where all values within a given continuous range are equally likely. This is the correct answer for a random variable that can assume any value within a specified range with equal likelihood.

So, the correct answer is:

Continuous uniform distribution

Would you like more details or have any questions?

Here are 8 related questions to expand on this topic:

1. What is the probability density function (PDF) of a continuous uniform distribution?
2. How do you calculate the mean and variance of a continuous uniform distribution?
3. What are some real-life examples of continuous uniform distributions?
4. How does the cumulative distribution function (CDF) of a continuous uniform distribution look?
5. Can a continuous uniform distribution be used to model waiting times?
6. How does a discrete uniform distribution differ from a continuous uniform distribution?
7. What is the role of parameters in defining a continuous uniform distribution?
8. How do you generate random samples from a continuous uniform distribution?

Tip: Understanding the properties and applications of different probability distributions can significantly enhance your ability to model and analyze random phenomena effectively.