What is the mean of a discrete random variable?

Solution:

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

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_ip_i = x₁p₁ + x₂p₂ + x₃p₃..........x_np_n 

where, Σ denotes the summation

Thus,

u_x = x₁p₁ + x₂p₂ + x₃p₃..........x_np_n

Hence, the mean of a discrete random variable is equal to u_x = x₁p₁ + x₂p₂ + x₃p₃..........x_np_n   = Σ x_ip_i

What is the mean of a discrete random variable?

Summary:

The mean of a discrete random variable is given by u_x = x₁p₁ + x₂p₂ + x₃p₃..........x_np_n   = Σ x_ip_i