1. What is Uniform Distribution?

The uniform distribution is a probability distribution where all outcomes are equally likely within a defined range [a, b]. It's characterized by a constant probability density function (PDF).

2. How Does the Calculator Work?

The calculator uses the uniform distribution PDF formula:

Where:

• \( a \) — Lower bound of the distribution
• \( b \) — Upper bound of the distribution
• \( f(x) \) — Probability density at point x (dimensionless)

Explanation: The PDF is constant between a and b, and zero elsewhere. The area under the curve always equals 1.

3. Importance of Uniform Distribution

Details: Uniform distribution is fundamental in probability theory and statistics, used in random number generation, Monte Carlo methods, and when modeling complete uncertainty within bounds.

4. Using the Calculator

Tips: Enter the lower bound (a) and upper bound (b) values. The calculator will compute the constant PDF value between these bounds. Ensure b > a for valid results.

5. Frequently Asked Questions (FAQ)

Q1: What does the uniform distribution represent?
A: It represents a situation where all values within a range are equally likely to occur.

Q2: What's the difference between discrete and continuous uniform distribution?
A: Discrete uniform has countable outcomes (like dice rolls), while continuous uniform has uncountable outcomes in a range.

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: Where is uniform distribution used in real life?
A: In random number generation, quality control, and when modeling complete uncertainty within known bounds.