• Sign In
• Blog
• Write for Us      Uh Oh! It seems you’re using an Ad blocker!

We always struggled to serve you with the best online calculations, thus, there's a humble request to either disable the AD blocker or go with premium plans to use the AD-Free version for calculators.

Or # Expected Value Calculator

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

Enter Values for X (Separated by Comma)

Enter Values for P(X) (Separated by Comma)

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 X Y

Table of Content

 1 What Is A Board Foot In Lumber (BF)? 2 Board Foot Formula: 3 Board Foot Units: 4 Important Thickness: 5 How To Calculate Board Feet? 6 What do you mean by the term “Surface Measure”? 7 What is meant by nominal measurement? 8 How do you define lineal measurement?

Get the Widget!

Add this calculator to your site and lets users to perform easy calculations.

Feedback

How easy was it to use our calculator? Did you face any problem, tell us!

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

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.

## References:

From the authorized source of Wikipedia : Definition & formula

From the source of Investopedia : General understanding of EV