Expected Value Calculator

Our expected value calculator helps to find the probability expected value of a discrete random variable (X) and give you accurate results.

What is Expected Value?

In probability and statistics theory, the expected value is exactly what you might think it means intuitively: it is referred to as the return that you can expect for some kind of action, like how many multiple-choice questions you might get right if you guess on a multiple-choice test. The expected value of a random variable (X) denoted (E(X)) or (E[X]), uses probability to tell what outcomes to expect in the long run.

What is the Expected Value Formula?

The formula for expected value (EV) is:

E(X) = mu_x = x₁P(x₁) + x₂P(x₂) + ... + x_nPx_n

E(X) = μ_x = Σⁿ_(i=1) x_𝑖 * P(x_𝑖)

where;

• E(X) is referred to as the expected value of the random variable X
• 𝜇_x is indicated as the mean of X
• ∑ is the symbol for summation
• P(x_𝑖)is indicated as the probability of the outcome x_𝑖
• x_𝑖 is referred to as the 𝑖^th outcome of the random variable X
• n is the number of possible outcomes
• 𝑖 is indicated as the possible outcome of the random variable X

How To Find Expected Value (Step-by-Step)

The formula is discussed earlier; here we have an example for a better understanding of the concept.

Example:

If the numbers are (4,8,6,3) and the probability of each value is (0.1, 0.5, 0.04) and (0.36) respectively. Find the expected value ?

Solution:

Let's add the values into the expected value formula:

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

Here,

X₁ = 4 and P(x₁) = 0.1

X₂ = 8 and P(x₂) = 0.5

X₃ = 6 and P(x₃) = 0.04

X₄ = 3 and P(x₄) = 0.36

So,

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

How Our Expected Value Calculator Works?

• Input the different “Outcomes” and their associated “Probabilities” in the respective fields
• Press the “Add Row” button if you have more values to generate new rows
• Press the “Calculate” button and that's all, you will get the expected value, expected value table and a step-by-step calculation

References:

From the authorized source of Wikipedia : Definition and formula
From the source of Investopedia : General understanding of EV