Introduction: Understanding the expected value of a probability distribution is crucial in statistics and probability theory. It represents the average or mean outcome of a random variable over multiple trials.
Formula: The expected value (EV) is calculated using the formula:
EV=∑i=1nxi⋅P(xi)
How to Use:
- Enter the number of events in the designated field.
- Input the probabilities for each event, separated by commas.
- Click the “Calculate” button to get the expected value.
Example: Suppose you have a six-sided die. The events are the numbers 1 through 6, each with a probability of 1661. Entering 6 for the number of events and “0.1667, 0.1667, 0.1667, 0.1667, 0.1667, 0.1667” for probabilities should yield an expected value of 3.5.
FAQs:
- Q: What is the Expected Value? A: The expected value is the average outcome of a random variable.
- Q: How is the Expected Value calculated? A: It’s calculated by multiplying each outcome by its probability and summing up the results.
- Q: Can I use decimals for probabilities? A: Yes, probabilities can be entered as decimals, just ensure they sum to 1.
- Q: What happens if I input negative probabilities? A: Probabilities must be non-negative; negative values are not valid.
- Q: Is there a limit to the number of events I can enter? A: No strict limit, but ensure the sum of probabilities matches the number of events.
Conclusion: This Expected Value of Probability Distribution Calculator simplifies the process of finding the average outcome in a given probability scenario. Whether you’re a student or a professional dealing with statistical data, this tool can save time and provide accurate results.