A few basic stats
     • Expected value of a random variable – 
        –example of Bernoulli and Binomal
     • Variance of a random variable
        –example of Bernoulli and Binomial
     • Correlation coefficient (same as Pearson correlation 
       coefficient)
     • Formulas:
        –Covariance(X,Y) = E((X-μ )(Y-μ ))
                                X    Y
        –Correlation(X,Y)= Covariance(X,Y)/σ σ
                                          X Y
        –Pearson correlation  
    Correlation between variables
  • Measures the correlation between two variables
  • The correlation r is between -1 and 1. A value of 
   1 means perfect positive correlation and -1 in 
   the other direction
  • The function f(r)  has a t-distribution with n-2 df 
   that can be used to obtain a p-value
          f(r)=r n- 2
              1- r2
     Pearson correlation coefficient
                                From Wikipedia
       Basic stats in Python
  • Mean and variance calculation
   –Define list and compute mean and variance
  • Correlations
   –Define two lists and compute correlation
      Statistical inference
  • P-value
  • Bayes rule
  • Posterior probability and likelihood
  • Bayesian decision theory
  • Bayesian inference under Gaussian 
   distribution
  • Chi-square test, Pearson correlation 
   coefficient, t-test