Answer:
See explanation below.
Step-by-step explanation:
If we have a continuous variable the expected value is defined as:
[tex] E(X) = \mu = \int_{a}^b x f(x) dx[/tex]
Where a and b are the limits for the distribution and [tex] f(x) [/tex] represent the density function.
If we have a discrete random variable X, the expected value is defined as:
[tex] E(X) = \sum_{i=1}^n x_i P(X_i)[/tex]
The mean is the most common measure of central tendency in order to describe a probability distribution.
The expected value also represent the first central moment of the random variable defined as:
[tex] \mu_1= E[(X-E[X])^1] =\int_{-\infty}^{\infty} (x-\mu)^n f(x) dx[/tex]
If we assum that X is a continuous random variable.
