Introduction to Statistics
Data collected and descriptive statistics: organization and description of data. Populations and samples. Normal samples.
Elements of probability
Combinatorial analysis. Introduction to the concept of probability. Sample space and events. Axioms and properties of probability. Conditional probability. Theorem of total probability and Bayes' formula. Independent events.
Models of random variables
Analysis of some one-dimensional random variables: Bernoulli random variables, binomial, hypergeometric, Poisson, geometric, rectangular, normal, exponential, gamma, chi-square, Student's t. Approximations.
Multivariate random variable
Joint distribution for discrete random variables. The multinomial distribution. Independent random variables. Conditional distributions. Joint distributions of functions of random variables. Covariance and correlation.
The distribution of sample statistics
Sampling and statistics. The sample mean. Limit theorems. The sample variance. The distributions of the statistics of normal populations.
Parameter estimation
Point estimates of parameters: research methods. Estimators and their properties. Interval estimation: confidence intervals (normal case).