To talk about an introduction to **econometrics**, it is necessary to establish the **mathematical and statistical foundations** to understand it. Starting from the summation:

- The
**symbol Σ is the Greek capital letter sigma**and means “the sum of”. - The
**letter i is called the summation index**; this letter is arbitrary and can also appear as t, j or k. **The expression ∑(i=1)^n**is read as the sum of**Xn**‘s terms from i equal to one up to n.- The
**numbers i and n**are the lower bound and upper bound of the summation.

## Rules of the addition operation

- A random variable is a variable whose value is unknown until it is observed.
- A discrete random variable can only take a limited or countable number of values.
- A continuous random variable can take any value in an interval.
- The population is the set of individuals who have certain characteristics and are of interest to a researcher.
- The sample is a subset of the population.

## Population and sample moments

The sample mean, mean or expected values:

A monotonic relationship is one of the following:

- When the value of one variable increases, so does the value of the other.
- When the value of one variable decreases, the value of the other variable decreases.

Let’s look at the following examples of monotonic and non-monotonic relationships:

Expected values of the functions of a random variable

## Some important probability distributions

Normal or Gaussian; if X is a **normally distributed random variable **with mean 𝝻 and variance **σ ^{2}**, it can be symbolised as

**X~N(𝝻,σ**)

^{2}**Chi-square**: If X, is a **normally distributed random variable** with mean **0** and variance **σ ^{2}**, then

**V= X**

_{1}^{2}+X_{2}^{2}+…+X_{m}^{2}~ X(_{m})^{2}A **Student’s random variable** is formed by dividing a **standard normal random variable** with mean 0 and variance 1 by the square root of an independent** chi-squared random variable**, V, divided by its m degrees of freedom.