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;
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:
Outputs:
Once you fill in the fields, the calculator shows:
From the authorized source of Wikipedia : Definition & formula
From the source of Investopedia : General understanding of EV