1. What is Uniform Distribution Variance?

The variance of a uniform distribution measures how spread out the values are between the lower and upper bounds. In a continuous uniform distribution, all values between the bounds are equally likely.

2. How Does the Calculator Work?

The calculator uses the uniform distribution variance formula:

Where:

• \( a \) — Lower bound of the distribution
• \( b \) — Upper bound of the distribution (must be greater than a)

Explanation: The variance increases with the square of the range between the bounds, divided by 12.

3. Importance of Uniform Distribution Variance

Details: Understanding the variance helps in probability analysis, quality control, and Monte Carlo simulations where uniform distributions are used.

4. Using the Calculator

Tips: Enter the lower and upper bounds of your uniform distribution. The upper bound must be greater than the lower bound.

5. Frequently Asked Questions (FAQ)

Q1: What does uniform distribution variance represent?
A: It quantifies how much the values in the distribution deviate from the mean, which is (a + b)/2 for uniform distribution.

Q2: What's the standard deviation of uniform distribution?
A: The standard deviation is the square root of the variance: \( \sqrt{\frac{(b - a)^2}{12}} \).

Q3: Can variance be negative?
A: No, variance is always non-negative as it's an average of squared deviations.

Q4: What happens when a = b?
A: When bounds are equal, variance is zero (all values are identical).

Q5: Where is uniform distribution used?
A: In simulations, random number generation, and when modeling situations where all outcomes are equally likely.