1. What is Discrete Uniform Distribution?

The discrete uniform distribution is a symmetric probability distribution where a finite number of outcomes are equally likely to occur. Each outcome has the same probability of 1/k, where k is the number of possible outcomes.

2. How Does the Calculator Work?

The calculator uses the discrete uniform distribution formula:

Where:

• \( P \) — Probability of each outcome (dimensionless)
• \( k \) — Number of possible outcomes (dimensionless)

Explanation: For a discrete uniform distribution with k outcomes, each outcome has an equal probability of 1/k.

3. Applications of Discrete Uniform Distribution

Details: This distribution is commonly used in games of chance (dice, roulette), random sampling, and cryptography. It's the simplest discrete probability distribution.

4. Using the Calculator

Tips: Enter the number of possible outcomes (k). The value must be a positive integer (k ≥ 1).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between discrete and continuous uniform distribution?
A: Discrete uniform has finite countable outcomes, while continuous uniform has infinite possible outcomes in a range.

Q2: What are some real-world examples?
A: Fair dice (k=6), coin toss (k=2), roulette wheel (k=37 or 38), lottery numbers.

Q3: What is the expected value for this distribution?
A: For outcomes numbered 1 to k, the expected value is (k+1)/2.

Q4: What is the variance of this distribution?
A: For outcomes numbered 1 to k, the variance is (k²-1)/12.

Q5: Can this be used for non-numeric outcomes?
A: Yes, as long as the outcomes are distinct and equally likely, they can be any type (colors, names, etc.).