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Statistics Calculators ▶ Expected Value Calculator

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**Table of Content**

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

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.

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 \(X\)

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,

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

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

\(E(X) = 5.72\)

**Inputs:**

- 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