1. What is Continuous Uniform Distribution?

The continuous uniform distribution is a probability distribution where all intervals of the same length are equally probable. It's defined by two parameters: the minimum (a) and maximum (b) values.

2. How Does the Calculator Work?

The calculator uses the uniform distribution probability density function:

Where:

• \( a \) — Lower bound of the distribution
• \( b \) — Upper bound of the distribution

Explanation: The probability density is constant between a and b, and zero elsewhere.

3. Importance of Uniform Distribution

Details: The uniform distribution is fundamental in probability theory and is used when all outcomes are equally likely, such as in random number generation.

4. Using the Calculator

Tips: Enter the lower bound (a) and upper bound (b) values. The upper bound must be greater than the lower bound.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between continuous and discrete uniform distribution?
A: Continuous uniform distribution applies to continuous variables over an interval, while discrete applies to a finite set of distinct values.

Q2: What are common applications of uniform distribution?
A: Used in simulations, random sampling, and as a prior distribution in Bayesian statistics when no prior information is available.

Q3: What is the mean of a uniform distribution?
A: The mean is (a + b)/2, the midpoint of the interval.

Q4: What is the variance of a uniform distribution?
A: The variance is (b - a)²/12.

Q5: Can the bounds be negative?
A: Yes, the bounds can be any real numbers as long as b > a.