Expected Value Calculator

Expected value

What is Expected Value?

The Expected Value (EV) is the Predicted Value for using at any point in the future. This value is also known as expectation, the average, the mean or the first moment. This is mainly used in statistics and probability analysis. This value is calculated by multiplying possible results by the likelihood of every result will appear and then take gross of all these values. By finding the expected values, users can easily choose the scenarios to get their desired results.

Example

For calculating single discrete random variables of Expected Value, one must multiply the value of the variable by the probability of that value occurring. For example, five players playing spin the bottle. Once you spin the bottle, it has an equal one-fifth chance to stop on one, two, three, four or five players. Random Variable gives its weighted average. Provide this information, the calculation is very simple

$$X\;=\;\text{Number of Players}\;=\;{1,2,3,4,5}$$

$$\text{Weighted Average}\;=\;(\frac{1}{5}* 1) + (\frac{1}{5} * 2) + (\frac{1}{5} * 3) + (\frac{1}{5} * 4) + (\frac{1}{5} * 5)$$

$$\text{Weighted Average}\;=\;0.2\;+\;0.4\;+\;0.6\;+\;0.8\;+\;1$$

$$\text{Weighted Average}\;=\;3.0$$

If you spin the bottle an infinite number of times, you’ll observe that the average value equals 3.0.

What is Expected Value Calculator?

This online expected value calculator will help you to find the expected value swiftly and easily of a discrete random variable X. By using this calculator, you will get detailed solutions to your problems. Also, you can understand how the algorithm is used by a calculator to find the discrete random variable’s expected value. Give the number of the probability of success and values of x, expected value calculator will notify you about the expected value for a discrete random variable.

How to Calculate Expected Value by using Expected Value Calculator?

This Expected Value Calculator finds the expected value of a set of numbers or a number which is based on the probability of that number or numbers occur.

Step 1:

Enter all known values of Probability of x P(x) and the Value of x in white shaded boxes. Enter all values in numeric form and separated them by commas.

Step 2:

Click the “Calculate” button and results will represent the Expected Value.

How Expected Value Formula works?

The formula used for how to find expected value for a number or set of numbers is defined as

$$\text{Expected Value}\;=\;\text{Sum of their associated probability}\;*\;\text{All possible outcomes}

$$\text{EV}\;=\;\sum P(X_i)\;*\;X_i$$

EV = Expected Value of an Opportunity
P(Xi) = Probability
Xi = All Possible Outcomes

This formula shows that for every value of X in a group of numbers, we have to multiply every value of x by the probability of that number occurs, by doing this we find the expected value.

Understanding the Expected Value

Scenario Analysis is the process of interpreting future events by estimating different possible outcomes. This Scenario Analysis is a technique for finding the expected value of the investment opportunity. It uses approximate probabilities with multiple variables to find the possible outcomes for a suggested investment. It also helps users to find whether they are taking a suitable level of risk providing the likely results of the investment.

The Expected Value of a random variable always calculated as the center of distribution of the variable. Most importantly this value is the variables long-term average value. Expected Value is calculated for single discrete variables, multiple discrete variables, single continuous variables, and multiple continuous variables.

Being known that by calculating expected values, expected outcomes of probabilities are calculated off a set of numbers, and the individual probabilities cumulatively sum up to 1 or 100%. Also, remember that none of the probabilities for any set of numbers is greater than 1. This is because any events happenings probabilities can’t be greater than 100%. So that’s why if any of the event probability is greater than 1 calculator shows an error message. Every time the total possible result is 100%. Therefore, there is not a single possibility of having a probability greater than 1 in any event or total of all events.

Advantages:

  • Measures center of the Probability distribution
  • Long term investment of variable
  • Reduces information to one possibility /answer
  • Allows us to anticipate future outcomes

Disadvantages

  • The risk rate is high as it ignores the risk
  • The difficulty for assessing probabilities of different results
  • Unacceptable for one-off decisions

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