Probability and Statistics

Probability and Statistics

1. Distribution Functions

   • Binomial
     • it has parameters, size of sample \[n\] and probabilitity of succes in percentage %.  Binom(n, proba)
   • Normal
     • It has parameters mean value \[\bar{x}\] and variance \[\sigma\]
   • Bernoulli
   • Exponential
   • Poisson
   • Beta
     • it has parameters \[ \alpha, \beta\]
   • Uniform

2. Counting Techniques

   • Combinatory
   • Permutations
   • Variations

3. Statistical Parameters

   • Measures of Centrality
     • Mean
     • Median
     • Mode
   • Measures of Dispersion
     • Standard Deviation
     • Range
       • Percentiles
       • Quartiles
       • Outliers
         • IR = Range between Q1 and Q3 IR = Q3 - Q1 Lim_inf = Q1 - 1.5*IR Lim_sup = Q3 - 1.5*IR outlier = x not in [Lim_inf, Lim_sup] 7
     • Variance
     • Mean Absolute Deviation
       • MAE
     • Correlation Coeficient
       • R^2
         • \[ R^2 = \frac{var(mean)-var(fit)}{var(mean)}\] \[var(mean)\] variation around the mean line of the y-value \[var(fit)\] variation around the fitted line to data
   • Measures of Position
     • Quartiles
     • Percentiles
     • Deciles

4. Data Distribution

   • Frequency Tables
     • Relative Frequency
     • Absolute Frequency
     • Cumulative Frequency

5. Laplace Rule

   • Probabilidad de que ocurra A \[ P(A) = \frac{ocurrencias \ de \ A}{numero \ de \ eventos } \]

6. Chain Rule (Probability)

   • Union
     • \[P(A \cup B) = P(A) + P(B) - P(A \cap B) \]
   • Intersection
     • \[P(A|B) = \frac{P(A \cap B)}{P(B)}\] donde \[ P(A \cap B) = P(A)\cdot P(B)\]

7. Bayes Theorem

   • \[P(A|B) = \frac{P(B|A)\cdot P(A)}{P(B)}\]
   • Bayesian Analysis
     • Bayesian Data analysis
     • Prior distribution
       • Prior information about the probability of the parameters of the model \[ P(\theta) \] where \[\theta\] are the parameter to calculated using prior information probability distribution
       • Uninformative Prior Distribution will be a Uniform Distribution Informative Prior Distributions could be any Distribution Function which describes the prior information before we have data
     • Posterior distribution
       • Posterior \[ P(\theta | D) \] Probability of different parameter values given the data D.
     • Generative Model
       • Generative model \[ P(D| \theta) \] What is the probability of data D, given the parameters \[\theta\]

8. Central Limit Theorem