# How To Find Expected Value

## How To Find Expected Value Statistics: It’s to Be Expected

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## How To Find Expected Value Get to grips with a basic Expected Value formula

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## How To Find Expected Value Video

Mean (expected value) of a discrete random variable - AP Statistics - Khan Academy

## How To Find Expected Value How to Get Best Site Performance

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 one-half of 3 is 1. We now turn to a continuous random variable, which we will denote by X. Here we see that the expected value of our random variable is expressed as an integral.

There are many applications for the expected value of a random variable. This formula makes an interesting appearance in the St.

Petersburg Paradox. Share Flipboard Email. Courtney Taylor. Professor of Mathematics. Courtney K. Taylor, Ph. Updated January 14, The expected value is what you should anticipate happening in the long run of many trials of a game of chance.

The carnival game mentioned above is an example of a discrete random variable. The variable is not continuous and each outcome comes to us in a number that can be separated out from the others.

To find the expected value of a game that has outcomes x 1 , x 2 ,. Why 8 and not 10? This means that over the long run, you should expect to lose on average about 33 cents each time you play this game.

Yes, you will win sometimes. But you will lose more often. Now suppose that the carnival game has been modified slightly.

In the long run, you won't lose any money, but you won't win any. Don't expect to see a game with these numbers at your local carnival. If in the long run, you won't lose any money, then the carnival won't make any.

Now turn to the casino. In the same way as before we can calculate the expected value of games of chance such as roulette.

In the U. Half of the are red, half are black. Both 0 and 00 are green. A ball randomly lands in one of the slots, and bets are placed on where the ball will land.

One of the simplest bets is to wager on red. If the ball lands on a black or green space in the wheel, then you win nothing. What is the expected value on a bet such as this?

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If the ball lands on a black or green space in the wheel, then you win nothing. What is the expected value on a bet such as this?

Here the house has a slight edge as with all casino games. As another example, consider a lottery.

This gives us an expected value of:. So if you were to play the lottery over and over, in the long run, you lose about 92 cents — almost all of your ticket price — each time you play.

All of the above examples look at a discrete random variable. However, it is possible to define the expected value for a continuous random variable as well.

All that we must do in this case is to replace the summation in our formula with an integral. It is important to remember that the expected value is the average after many trials of a random process.

In the short term, the average of a random variable can vary significantly from the expected value. Share Flipboard Email. Courtney Taylor.

Professor of Mathematics. This makes sense with our intuition as one-half of 3 is 1. We now turn to a continuous random variable, which we will denote by X.

Here we see that the expected value of our random variable is expressed as an integral. There are many applications for the expected value of a random variable.

This formula makes an interesting appearance in the St. Petersburg Paradox. Share Flipboard Email. Courtney Taylor.

Professor of Mathematics. Courtney K. Personal Finance. Your Practice. Popular Courses. Financial Analysis How to Value a Company.

What is the Expected Value EV? Compare Accounts. The offers that appear in this table are from partnerships from which Investopedia receives compensation.

Related Terms Random Variable A random variable is a variable whose value is unknown, or a function that assigns values to each of an experiment's outcomes.

How Binomial Distribution Works The binomial distribution is a probability distribution that summarizes the likelihood that a value will take one of two independent values.

Uniform Distribution Definition In statistics, uniform distribution is a type of probability distribution in which all outcomes are equally likely.

What Joint Probability Tells Us Joint probability is a statistical measure that calculates the likelihood of two events occurring together and at the same point in time.

Joint probability is the probability of event Y occurring at the same time that event X occurs. Bayes' Theorem Bayes' theorem is a mathematical formula for determining conditional probability.

How Discrete Distribution Works A discrete distribution is a statistical distribution that shows the probabilities of outcomes with finite values.

## How To Find Expected Value Video

Calculating Expected values and Chi Squared Values 1. Kajitilar says:
2. Moogukasa says: