Expectation and Moments/Part1

Expectation and Moment
Expectation Value of a Random variable
is the expectation of the random phenomenon, also sometimes called an expected value
In case of discret random variable ,the expectation of the this variable, which is as follows
E(X)= sum of the product of the values of this variable by its probability , that is the probability mass function.
In case of continuous random variable,the expectation of the this variable,
, which is as follows
E(X)= the integral of the product of the values of this variable by its probability , that is the probability density function.
In the discreet case of mathematical expectation formula, p(x) denotes the probability mass function and f(x), in the continuous case of mathematical expectation formula, denotes the probability density function.
The expectation of the sum of two random variables X and Y equal to the sum of the expectation values of those random variables.
We can generalize this property as follows:
The expectation of this sum of n random variables equal to the sum of the expectations of these variables.
The expectation of the product of n independent random variables equal to the product of the expectations these variables