
Determine Expected Value
Determine Expected Value How to Get Best Site Performance
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Expected Value ExcelLet's say that we repeat this experiment over and over again. Over the long run of several repetitions of the same probability experiment, if we averaged out all of our values of the random variable , we would obtain the expected value.
In what follows we will see how to use the formula for expected value. We start by analyzing the discrete case. Given a discrete random variable X , suppose that it has values x 1 , x 2 , x 3 ,.
The expected value of X is given by the formula:. Using the probability mass function and summation notation allows us to more compactly write this formula as follows, where the summation is taken over the index i :.
This version of the formula is helpful to see because it also works when we have an infinite sample space.
This formula can also easily be adjusted for the continuous case. Flip a coin three times and let X be the number of heads. The only possible values that we can have are 0, 1, 2 and 3.
Use the expected value formula to obtain:. In this example, we see that, in the long run, we will average a total of 1. This makes sense with our intuition as onehalf of 3 is 1.
We now turn to a continuous random variable, which we will denote by X. Log in Facebook. No account yet? Create an account. Edit this Article.
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Tips and Warnings. Things You'll Need. Related Articles. Article Summary. Method 1 of Identify all possible outcomes. Calculating the expected value EV of a variety of possibilities is a statistical tool for determining the most likely result over time.
To begin, you must be able to identify what specific outcomes are possible. You should either list these or create a table to help define the results.
You need to list all possible outcomes, which are: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, in each of four different suits. Assign a value to each possible outcome.
Some expected value calculations will be based on money, as in stock investments. Others may be selfevident numerical values, which would be the case for many dice games.
In some cases, you may need to assign a value to some or all possible outcomes. Assign those values for this example.
Determine the probability of each possible outcome. Probability is the chance that each particular value or outcome may occur. In some situations, like the stock market, for example, probabilities may be affected by some external forces.
You would need to be provided with some additional information before you could calculate the probabilities in these examples.
In a problem of random chance, such as rolling dice or flipping coins, probability is defined as the percentage of a given outcome divided by the total number of possible outcomes.
However, recognize that there are four different suits, and there are, for example, multiple ways to draw a value of Since your list of outcomes should represent all the possibilities, the sum of probabilities should equal 1.
Multiply each value times its respective probability. Each possible outcome represents a portion of the total expected value for the problem or experiment that you are calculating.
To find the partial value due to each outcome, multiply the value of the outcome times its probability. Multiply the value of each card times its respective probability.
Find the sum of the products. The expected value EV of a set of outcomes is the sum of the individual products of the value times its probability.
Using whatever chart or table you have created to this point, add up the products, and the result will be the expected value for the problem.
Interpret the result. The EV applies best when you will be performing the described test or experiment over many, many times.
For example, EV applies well to gambling situations to describe expected results for thousands of gamblers per day, repeated day after day after day.
However, the EV does not very accurately predict one particular outcome on one specific test. Over many many draws, the theoretical value to expect is 6.
But if you were gambling, you would expect to draw a card higher than 6 more often than not. Method 2 of Define all possible outcomes. Calculating EV is a very useful tool in investments and stock market predictions.
As with any EV problem, you must begin by defining all possible outcomes. Generally, real world situations are not as easily definable as something like rolling dice or drawing cards.
For that reason, analysts will create models that approximate stock market situations and use those models for their predictions. These results are: 1.
Earn an amount equal to your investment 2. Earn back half your investment 3. Neither gain nor lose 4. Lose your entire investment. Assign values to each possible outcome.
In some cases, you may be able to assign a specific dollar value to the possible outcomes. Other times, in the case of a model, you may need to assign a value or score that represents monetary amounts.
The assigned value of each outcome will be positive if you expect to earn money and negative if you expect to lose. Determine the probability of each outcome.
In a situation like the stock market, professional analysts spend their entire careers trying to determine the likelihood that any given stock will go up or down on any given day.
The probability of the outcomes usually depends on many external factors. Statisticians will work together with market analysts to assign reasonable probabilities to prediction models.
Multiply each outcome value by its respective probability. Use your list of all possible outcomes, and multiply each value times the probability of that value occurring.
Add together all the products. Find the EV for the given situation by adding together the products of value times probability, for all possible outcomes.
Interpret the results. You need to read the statistical calculation of the EV and make sense of it in real world terms, according to the problem.
Earning Method 3 of Familiarize yourself with the problem. Before thinking about all the possible outcomes and probabilities involved, make sure to understand the problem.
A 6sided die is rolled once, and your cash winnings depend on the number rolled.
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