1. What is Uniform Distribution?

A uniform distribution is a probability distribution where all outcomes are equally likely. In a continuous uniform distribution, every value between the lower bound (a) and upper bound (b) has equal probability density.

2. How Does the Calculator Work?

The calculator uses the uniform distribution mean formula:

Where:

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

Explanation: The mean of a uniform distribution is simply the midpoint between the lower and upper bounds.

3. Importance of Uniform Distribution

Details: Uniform distribution is fundamental in probability theory and statistics. It's used in simulations, random sampling, and as a basis for generating other probability distributions.

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 for valid results.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between discrete and continuous uniform distribution?
A: Discrete uniform distribution has a finite number of outcomes, while continuous uniform distribution has an infinite number of possible outcomes within the bounds.

Q2: What is the variance of a uniform distribution?
A: The variance is \( \frac{(b-a)^2}{12} \), where a is lower bound and b is upper bound.

Q3: Where is uniform distribution used in real life?
A: It's used in random number generation, quality control, and when modeling situations where all outcomes are equally likely.

Q4: What does the PDF of uniform distribution look like?
A: The probability density function is a rectangle with constant height between a and b, and zero elsewhere.

Q5: Can uniform distribution be asymmetric?
A: No, the standard uniform distribution is always symmetric about its mean, but the bounds can be any values as long as a < b.