1.1    Definition of set & Venn diagram
1.2    Operations with sets
1.3    De Morgan’s rule
1.4    Examples

2.1    Permutations: n! factorial
2.2    Combinations: the binomial & multinomial coefficients 
2.3    Stirling formula
2.4    Examples

3.1    Sample space and events
3.2    Kolmogorov theory: basic axioms of probability
3.3    Addition theorem
3.4    Conditional probability
3.5    Stochastic independence
3.6    Theorem of total probability
3.7    Bayes’s theorem
3.8    Examples

4.1    Discrete & continuous sample spaces
4.2    Moments: mean, variance, skewness and kurtosis
4.3    Characteristic function of a random variable
4.4    Tchebycheff's theorem
4.5    Useful probability distributions in engineering
4.6    Transformation of random variables

5.1   Joint, marginal and conditional pdf
5.2   Moments and covariances
5.3   Sum of random variables:  the chi-square distribution
5.4 Products and quotients of random variables : T-student distribution

6.1    A simple proof and applications

9.1    Statistical population and random samples
9.2    Parameter estimation
9.2.1    Statistics of the estimator
9.2.2    Unbiasedness, sufficiency and ergodicity of an estimator
9.3    Estimator of the mean
9.4    Estimator of the variance
9.5    The method of maximum likelihood
9.6    Interval estimation of the mean
9.7    Interval estimation of the variance
9.8    The Buffon’s needle problem revisited: an estimator for pi 

10.1    The least square principles ( LSP)
10.2    Linear regression by LSP
10.3    Linear regression interpreted in terms of conditional probability
10.4    Multivariate linear regression
10.5    Nonlinear regression

11.1    Definitions and sample space
11.2    The simple random walk
11.3    The Poisson process
11.4    The Gaussian process

12.1    Numerical proof of ergodicity for the estimator of the mean
12.2    The Buffon’s needle problem: : estimators for    and 
12.3    2D The random walk