1. What is Uniform Distribution Probability?

The uniform distribution describes an experiment where all outcomes are equally likely within a range [a, b]. The probability that a random variable X is less than some value x is calculated by the given formula.

2. How Does the Calculator Work?

The calculator uses the uniform probability formula:

Where:

• \( x \) — The value for which we calculate probability
• \( a \) — Lower bound of the distribution
• \( b \) — Upper bound of the distribution

Explanation: The formula calculates the proportion of the interval [a, b] that lies below x.

3. Importance of Uniform Distribution

Details: Uniform distribution is fundamental in probability theory and statistics, used in simulations, random sampling, and when modeling complete randomness.

4. Using the Calculator

Tips: Enter x between a and b, with b > a. The result will be a probability between 0 and 1.

5. Frequently Asked Questions (FAQ)

Q1: What does P(X < x) represent?
A: It represents the probability that a randomly selected value from the uniform distribution will be less than x.

Q2: What are typical applications of uniform distribution?
A: Used in random number generation, Monte Carlo simulations, and when modeling complete uncertainty about outcomes.

Q3: What's the difference between discrete and continuous uniform distribution?
A: Continuous has infinite possible values in [a,b], while discrete has a finite number of equally spaced values.

Q4: What is the expected value in uniform distribution?
A: The expected value is (a + b)/2, the midpoint of the interval.

Q5: What is the variance of uniform distribution?
A: The variance is (b - a)²/12, representing how spread out the values are.