1. Theme 8. Major probability distributions
1. Discrete random variables: binomial distribution.
2. Continuous random variables: normal distribution.
3. Continuous random variables: t distribution.
4. Continuous random variables: Chi Square distribution.
5. Continuous random variables: F distribution.

2. 8.1 Binomial distribution (discrete random variables)
It is used when:
  1. We have a number n of "experiments" (observations), all independent of each other.
2. In each of these "experiments”, there is a binary outcome (success [p] vs. failure [1-p])
3. The probability of "success" [p] is the same in every "experiment"
Expected value= n * p
With high values of n, this distribution approaches the normal distribution.

3. 8.2 Normal distribution (or Gaussian)
It is the best known distribution. Its density function is:
Where alpha can be any real number, and beta can be any positive real number; the first functions as mean and the second variance.

4. normal distribution (2)
It is symmetric and unimodal
Like any other continuous distribution, the area under the curve is 1 (remember that the curve is asymptotic to the X axis
standardized normal distribution
It is one that has mean 0 and variance 1. It can be expressed as N (0,1)

5. 8.3 Student t Distribution
It's symmetrical and unimodal, with mean 0
It's a family of curves, depending on the so-called "degrees of freedom". That is, there is a Student's t distribution with 1 df, Student's t-distribution with 2 df, etc.
-As the degrees of freedom increase, the t distribution tends more and more to a standardized normal distribution.
(It is used to contrast the means of two groups, etc.)

6. 8.4 Distribution chi-square
It never adopts negative values
It's positive asymmetrical
It's actually a family of curves, depending on the so-called "degrees of freedom". That is, there is a chi-square distribution with 1 df, chi-square distribution with 2 df, etc. (Note: The degrees of freedom are always positive numbers.)
-As the degrees of freedom increase, the distribution becomes more and more symmetrical.
When to use it: In tests of goodness of fit (when comparing the predicted scores with observed scores), for instance.

7. 8.5 Fisher’s F distribution (in some books "Snedecor’s F")
It can not adopt negative values
It's positive asymmetrical
It's actually a family of curves, depending on the so-called "degrees of freedom" of the numerator and denominator. That is, there is a Fisher F con1 gl in the numerator and 10 df in the denominator, etc.
- It can be shown that the distribution F corresponds to a ratio of two chi-square, hence we speak in the case of F degrees of freedom in the numerator and denominator.
(Analysis of Variance -ANOVA- among others)