Your Result is copied!

Expected Value Calculator

Please provide discrete random variable values along with probabilities to calculate the expected value through this calculator.

Change Input Style

Add this calculator to your site

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: $$ E(X) = \mu_x = x_{1}P(x_1) + x_{2}P(x_2) + ... + x_{n}P(x_n) $$ $$ E(X) = \mu_x = \sum_{i=1}^{n} x_i * P(x_i) $$ where;
  • \(E(X)\) is referred to as the expected value of the random variable \((X)\)
  • \(\mu_x\) is indicated as the mean of \(X\)
  • \(\sum\) 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 said to be as 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: \(E(X) = \mu_x = x_{1} P(x_1) + x_{2}P(x_2) + ... + x_{n}P(x_n)\) Here, \(X_1 = 4 \text { & } P(x_1) = 0.1\) \(X_2 = 8 \text { & } P(x_2) = 0.5\) \(X_3 = 6 \text { & } P(x_3) = 0.04\) \(X_4 = 3 \text { & } P(x_4) = 0.36\) 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

  • First of all, enter the values separated with commas for calculating expected value
  • Very next, enter the probability of each number in the designated field.
  • Lastly, hit the calculate button.
Outputs: Once you fill in the fields, the calculator shows:
  • Expected value.
  • Expected value table.
  • Step-by-step calculation.


From the authorized source of Wikipedia : Definition & formula From the source of Investopedia : General understanding of EV
Online Calculator



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

© Copyrights 2024 by