# How to find the expected value of a discrete random variable?

The expected value is equal to the sum of the product of each possible outcome with its probability and is expressed as the formula for the expected value.

## Answer: Expected Value of a discrete random variable is given by (E(*X*)) = Σ x P(*X* = *x*).

Let us understand the given problem step by step.

**Explanation: **

In a discrete random variable, the expected value is calculated by adding the value of the random variable and its associated probability, taking all the values of the random variable.

In symbols (E(*X*)) = Σ x P(*X* = *x*)

Let us understand better by taking the following example.

**Example**

Random variable *X* has the following probability function:

x | 0 | 1 | 2 | 3 |

P(X = x) | 0.2 | 0.4 | 0.8 | 0.6 |

E(*X*) = (0 × 0.2) + (1 × 0.4) + (2 × 0.8) + (3 × 0.6) = 3.8

Below is a bar graph of the probability function, labeled with the expected value.

### Thus,Expected Value of a discrete random variable is given by (E(*X*)) = Σ x P(*X* = *x*).

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