Calculator Online

Home AI Chat AI Math Solver

NEW

Tools ▾ Category ▾

Pricing Sign In

Calculator Online

Your Result is copied!

Expected Value Calculator

Enter the potential outcomes and their associated probabilities to calculate the expected value (mean) of a random variable. Ensure that the total probability sums to 1

X	P(x)

Add Row

	1	2	3	4	5	6	7	8	9	10	11	12	13	14
X
Y

Related

Our Expected Value Calculator helps determine the probability-weighted average outcome of a discrete random variable (X), providing accurate results for decision-making and probability analysis.

What is Expected Value?

The expected value represents the average outcome you can anticipate from a random event over the long run. It is the "return you can expect" from an action, like guessing on a multiple-choice test. The expected value of a random variable X, denoted E(X) or E[X], is calculated using probabilities of each possible outcome.

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

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 Our Expected Value Calculator Works

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)

Related

Calculator Online

Get the ease of calculating anything from the source of calculator online

Links

Home Conversion Calculator About Calculator Online Blog Hire Us Knowledge Base Sitemap Sitemap Two

Support

Email us at