Expected Value Calculator

Expected Value Calculator

Enter each outcome along with its probability to calculate the expected value (mean) of a random variable quickly and accurately. Make sure the total probability adds up to 1.

X	P(x)

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Expected Value Calculator:

This expected value calculator determines the average outcome of a random event when different outcomes have different probabilities. It multiplies each possible outcome by its probability and adds them together to calculate the long-term average value. For example, it can be used to estimate the average return in games, investments, or probability-based decisions.

What is Expected Value?

Expected value represents the average outcome you can expect from a random event over the long run. It is a measure of the expected result of an action or experiment based on the probabilities of all possible outcomes. The expected value of a random variable X, denoted as E(X) or E[X], is calculated by multiplying each possible outcome by its probability and then summing the results.

Expected Value Formula:

The expected value is calculated as:

E(X) = μ_x = x₁P(x₁) + x₂P(x₂) + ... + x_nP(x_n)

Or equivalently:

E(X) = μ_x = Σ_i=1ⁿ x_i * P(x_i)

E(X) – expected value of X
μ_x – mean of X
P(x_i) – probability of outcome x_i
x_i – the i^th outcome
n – total number of possible outcomes

How to Calculate the Expected Value?

Step-by-Step Example:

Suppose we have outcomes 4, 8, 6, 3 with probabilities 0.1, 0.5, 0.04, 0.36 respectively. Find the expected value.

Solution:

X₁ = 4, P(X₁) = 0.1
X₂ = 8, P(X₂) = 0.5
X₃ = 6, P(X₃) = 0.04
X₄ = 3, P(X₄) = 0.36

Substitute values into the formula:

E(X) = (4)(0.1) + (8)(0.5) + (6)(0.04) + (3)(0.36)

E(X) = 0.4 + 4 + 0.24 + 1.08

E(X) = 5.72

✅ Interpretation: The long-term average outcome is 5.72 if the experiment is repeated many times.

How to use the Expected Value Calculator?

Enter the Outcomes and their corresponding Probabilities.
Click "Add Row" to include more values if needed.
Press "Calculate" to get:
- The Expected Value
- A complete Expected Value Table
- Step-by-step calculation for clarity

References:

From Wikipedia: Definition and Formula of Expected Value.
From Investopedia: General Understanding of Expected Value (EV).