What Is a Free Expected Value Calculator?
A Free Expected Value Calculator is an online probability and statistics tool that calculates the expected value (EV) of a random event based on its possible outcomes and the probability of each outcome.
Expected value represents the long-run average result you would expect if the same random experiment were repeated many times.
E[X]=∑xxP(X=x)\mathbb{E}[X] = \sum_x xP(X=x)
E[X]=2(0.25)+8(0.75)=6.5\mathbb{E}[X]=2(\text{0.25})+8(\text{0.75})=\text{6.5}E[X]=2(0.25)+8(0.75)=6.5
Chance of outcome 8, P(X=8)
Chance of outcome 8, P(X=8)28P=0.25P=0.75E[X]
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Expected Value Formula
For a discrete random variable, the expected value is: E(X)=∑xP(x)E(X)=\sum xP(x)
Where:
- E(X) = expected value
- x = possible outcome
- P(x) = probability of that outcome
The probabilities of all possible outcomes should add up to 1 (or 100%).
Example
Suppose a game has these possible results:
| Outcome | Probability |
|---|---|
| $100 | 20% |
| $50 | 30% |
| $0 | 50% |
The expected value is: E(X)=(100)(0.20)+(50)(0.30)+(0)(0.50)E(X)=(100)(0.20)+(50)(0.30)+(0)(0.50) E(X)=20+15+0=$35E(X)=20+15+0=\$35
So, the expected value is $35 per game.
This does not mean you will receive exactly $35 in one game. It means that over many repetitions, the average outcome would tend toward $35.
What Is a Free Expected Value Calculator Used For?
An Expected Value Calculator can be useful for:
- Probability problems
- Statistics homework
- Decision-making
- Investment analysis
- Business forecasting
- Insurance calculations
- Game and lottery probability
- Risk analysis
- Expected profit and loss calculations
Expected Value in Decision Making
Expected value can help compare different choices by combining the potential outcome with its probability of occurring. A choice with a higher expected value may have a better long-term average outcome, although expected value does not measure risk by itself.
In simple terms: a Free Expected Value Calculator quickly determines the weighted average of possible outcomes according to their probabilities, helping you understand the likely long-term average result of a random event.
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