Expected Value Calculator

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)

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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