Expected Value Definition, Formula, and Examples

Expected value is a concept in probability theory that describes the average value of a random variable. It is a measure of central tendency, and is calculated by taking the sum of all possible outcomes of a random variable, weighted by their probabilities.

The expected value of a random variable X is denoted by E(X). It is calculated as follows:

```
E(X) = Sx*P(x)
```

where x is an outcome of the random variable X, and P(x) is the probability of that outcome.

For example, if you flip a coin, the possible outcomes are heads and tails. The probability of heads is 1/2, and the probability of tails is 1/2. The expected value of the coin flip is therefore (1/2)*1 + (1/2)*0 = 0.5.

Expected value is a useful concept in finance because it can be used to make decisions about risky investments. For example, if you are considering investing in a stock, you can use the expected value of the stock's returns to determine whether or not it is a good investment.

The expected value of a stock's returns is calculated by taking the sum of all possible future returns of the stock, weighted by their probabilities. This gives you a sense of the average return you can expect to earn from the investment.

Of course, there is no guarantee that you will actually earn the expected return. However, the expected value can be used to make an informed decision about whether or not to invest in the stock.

Here are some additional examples of expected value:

* The expected value of a dice roll is 3.5.
* The expected value of a coin flip is 0.5.
* The expected value of a lottery ticket is negative.

Expected value is a fundamental concept in probability theory and finance. It is a useful tool for making decisions about risky investments.