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# 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

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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:

$$E(X) = \mu_x = x_{1}P(x_1) + x_{2}P(x_2) + … + x_{n}P(x_n)$$

$$E(X) = \mu_x = \sum_{i=1}^{n} x_i * P(x_i)$$

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