# What is the mean of a discrete random variable?

We will use the concept of probability and random variables to find the mean of discrete random variables.

## Answer: The mean of a discrete random variable is given by u_{x} = x_{1}p_{1 }+ x_{2}p_{2 }+ x_{3}p_{3}..........x_{n}p_{n }= Σ x_{i}p_{i}

Lets see how we will use the concept of probability and random variables to find the mean of discrete random variables.

**Explanation:**

The mean of a discrete random variable X is defined as the weighted mean of every possible value that the random variable can take.

The mean of a discrete random variable weights each random variable as x_{i }in accordance with its probability p_{i}. The symbol for the mean of a discrete random variable is u_{x}.

Thus, the mean is given as the sum of the product of x_{i }and p_{i} values as shown below:

Σ x_{i}p_{i} = x_{1}p_{1 }+ x_{2}p_{2 }+ x_{3}p_{3}..........x_{n}p_{n }

where, Σ denotes the summation

Thus,

u_{x} = x_{1}p_{1 }+ x_{2}p_{2 }+ x_{3}p_{3}..........x_{n}p_{n}

### Hence, the mean of a discrete random variable is equal to u_{x} = x_{1}p_{1 }+ x_{2}p_{2 }+ x_{3}p_{3}..........x_{n}p_{n }= Σ x_{i}p_{i}

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