Learning Outcomes
Upon successful completion of the course students will be able to:
1. calculate the marginal random variables of a multidimensional random variable;
2. calculate the conditional random variables of a multidimensional random variable;
3. calculate moments of multidimensional random variables;
4. calculate and use the moment generator function of a multivariate random variable;
5. use/apply the Central Limit Theorem.
Course Content (Syllabus)
The algebra of events - Probability Space - The axioms of Probability -
Random variables - The notion of stochastic distribution - Multidimensional random
variables - Multidimensional distribution functions - Marginal distributions -
Denumerable multidimensional random variables - Continuous multidimensional
distributions - Multidimensional normal distribution - Stochastic independence -
Conditional Probability - Conditional density - Conditional distributions - Mean values
for multidimensional random variables - Conditional mean values - Regression line -
Mean square error - Random variable transforms - Compound distributions - Inequalities
- Multiple Correlation coefficient - Ordered random variables - Characteristic functions -
The sum of independent random variables - Characteristic functions of multidimensional
random variables - Moment generating functions - Probability generating functions -
Limit theory of random variables - Convergences - Relations between convergences -
Central Limit Theorem - Laws of large numbers - The log log law.
Keywords
Multidimensional random variables, Conditional Probability, Random variable transform, Convergences, Central Limit Theorem