1. What is Dice Roll Statistics?

The expected value in dice roll statistics represents the average outcome you would expect over many trials. It's calculated by dividing the sum of all rolls by the number of rolls.

2. How Does the Calculator Work?

The calculator uses the expected value formula:

Where:

• \(\sum \text{Rolls}\) — Sum of all dice roll results
• \(n\) — Number of dice rolls

Explanation: This simple formula gives the arithmetic mean of all dice rolls, which is the most common measure of central tendency.

3. Importance of Expected Value

Details: The expected value helps predict long-term averages in probability experiments like dice rolling, and is fundamental in probability theory and statistics.

4. Using the Calculator

Tips: Enter the total sum of all dice rolls and the number of rolls. Both values must be positive numbers (sum ≥ 0, n > 0).

5. Frequently Asked Questions (FAQ)

Q1: What does the expected value represent?
A: It represents the long-term average value of repetitions of the experiment it represents (e.g., dice rolls).

Q2: How is this different from probability?
A: Probability describes likelihood of single events, while expected value describes the average outcome over many trials.

Q3: Does this work for biased dice?
A: Yes, as long as you input the actual sum and number of rolls, it will calculate the empirical average.

Q4: What's the expected value for a single fair die?
A: For a standard 6-sided die, the theoretical expected value is 3.5 (1+2+3+4+5+6 divided by 6).

Q5: Can I use this for other discrete probability distributions?
A: Yes, this formula works for calculating the sample mean of any discrete outcomes, not just dice rolls.