1. What is Expected Value?

The expected value (E[X]) is a fundamental concept in probability that represents the average outcome if an experiment is repeated many times. It's calculated by summing all possible values multiplied by their respective probabilities.

2. How Does the Calculator Work?

The calculator uses the expected value formula:

Where:

• \( x \) — Possible outcome value
• \( P(x) \) — Probability of that outcome
• \( \sum \) — Sum over all possible outcomes

Explanation: Each outcome's contribution to the average is weighted by its probability of occurring.

3. Importance of Expected Value

Details: Expected value is crucial in decision theory, statistics, finance, and many real-world applications like insurance, gambling, and risk assessment.

4. Using the Calculator

Tips: Enter each possible outcome value and its probability (between 0 and 1). You can add more rows as needed. The sum of probabilities should ideally equal 1.

5. Frequently Asked Questions (FAQ)

Q1: What if my probabilities don't sum to 1?
A: The calculator will still work but will show a warning. For proper probability distributions, the sum should be 1.

Q2: Can I use percentages instead of decimals?
A: No, probabilities must be entered as decimals between 0 and 1 (e.g., 50% = 0.5).

Q3: What does a negative expected value mean?
A: It indicates that on average, you would lose that amount per trial in the long run.

Q4: How is expected value different from mean?
A: They're conceptually similar, but expected value refers to theoretical probability distributions while mean refers to actual observed data.

Q5: Can expected value be outside the range of possible outcomes?
A: Yes, expected value can be higher or lower than any individual possible outcome.