Mathematics A3 for Chemical Engineers and Bioengineers

Algebra of events. Combinatorial problems. Probability. Independence of events. Conditional probability. Theorem of total probability, Bayes rule. Definition of random variables. Properties of random variables, expectations, moments, variances, median. Distributions, mass functions and densities. Inequality of Chebysew, the Weak Law of Large Numbers. Some discrete distributions: binomial, geometric, Poisson. Applications, Poisson process. Some continous distribution: uniform, exponential, normal.  Applications. Poisson limit theorem, approximation of binomial distribution by normal distribution. Moivre-Laplace theorem. Multiple random variables. Joint and marginal distributions, mass functions and densities. Independence. Stochastic processes. Covariances and correlations. Multivariate normal distributions. Conditional distributions, conditional density functions. Regression. Descriptive statistics, sampling distributions
associated with the normal population. Techniques for finding point estimators for parameters, Maximum Likelihood Method. Criteria for evaluating the goodness of estimators, sufficiency. Techniques for finding interval estimators for parameters. Test of statistical hypothesis. Applications.