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Expected Value Calculator

Expected Value Calculator

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An online expected value calculator helps to find the probability expected value (mean) of a discrete random variable (X). Remember that expected value calculation helps to reduce the information to one possibility/answer.

Knock out the content thoroughly to know how to calculate expected value, its formula, and some basics you should beware of.

Also, you can try our online mean calculator that helps you to determine the mean, mode, median & the range of the data set.

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 \(X\)

Our expected value calculator also uses the same equation for calculating \(E(X)\) and its table.

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,

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

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

\(E(X) = 5.72\)

As it measures the expected outcome of the probability of a set of numbers so, the individual probabilities must collectively add up to 1 or 100%. Also, none of any probability can be greater than 1. Because the probability of any event happening cannot be greater than 100%. That’s why the expected value calculator displays an error message if any event or collectively probability is greater than 1.

Understanding the Expected Value (EV):

There is a technique of scenario analysis for calculating the EV of an investment. It uses the probabilities with different models to examine the possible outcomes for the purposed investment. The EV is also known as expectation, mean or first moment. It can be calculated for single variables (discrete or continuous) & multiple variables (discrete or continuous).

How to Use the Online Expected Value Calculator:

Get handy calculations with the assistance calculator for expected value, just enter the exact value to calculate better outcomes, take a look right now!

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.

Advantages & Disadvantages of Expected value:

Advantages:

  • Reduces information to one answer.
  • Long term investment of variable.
  • Measure central of probability distribution.
  • Expectations of future outcomes.

Disadvantages:

  • Risk rate is high.
  • Difficult to determine probabilities.
  • Unacceptable for one-off decisions.

End-Note:

In statistics & probability analysis, the expected value is indicated as an ideal way to make a decision as it lets quantify and incorporate risk into decision making. Additionally, this mean value assists to balance potential and bad outcomes in the same equation – remember good and bad outcomes are both possible. Unfortunately, finding expected value is a nightmare for non-statistician. Thus, calculator-online provides the free online expected value calculator to do E(X) calculations for a number or data set values.

References:

From the authorized source of Wikipedia : Definition & formula

From the source of Investopedia : General understanding of EV

From the source of kfknowledgebank : Pros & Cons of expected value