1. What Is Expected Rate?

The expected rate is the weighted average of possible rates, where each rate is multiplied by its probability of occurrence. It represents the mean value you would expect to see over many trials.

2. How Does The Calculator Work?

The calculator uses the expected rate equation:

Where:

• \( p \) — Probability of each outcome (must sum to 1)
• \( rate \) — Rate associated with each outcome

Explanation: The equation calculates the weighted average of all possible rates, with probabilities as weights.

3. Importance Of Expected Rate Calculation

Details: Expected rate is fundamental in probability theory, finance, risk assessment, and decision making under uncertainty.

4. Using The Calculator

Tips: Enter at least one probability-rate pair. Probabilities should be between 0 and 1, and the sum of all probabilities should ideally equal 1 for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What if my probabilities don't sum to 1?
A: The calculator will still work, but the interpretation changes - it assumes the remaining probability has a rate of 0.

Q2: Can I add more than two probability-rate pairs?
A: This basic calculator handles two pairs. For more complex calculations, you would need to extend the formula.

Q3: What units should the rates be in?
A: The rates can be in any units (percentages, dollars, etc.), but all rates should be in the same units.

Q4: How is this different from a simple average?
A: Expected rate weights each value by its probability, while a simple average gives equal weight to all values.

Q5: Where is this calculation commonly used?
A: Common applications include finance (expected returns), insurance (expected claims), and statistics (expected values).