The first objective of the course is to help the student to learn and understand of the basic concepts descriptive statistics (univariate and bivariate). These concepts include measures of centralization, dispersion and shape, basic graphics as histograms and boxplots, and scatterplots that relate the concepts of covariance and correlation. Secondly, some probability notions are introduced, like the definition of probability, one-dimensional random variables and their moments, with special attention to classical distributions, such as binomial, Poisson, uniform, exponential, normal among others. Finally, some methods of point and interval estimation are presented in order to determine the values of the parameters of the previously studied probability distributions. As a particular case, the sample mean distribution is obtained and studied.
1.1. Concepts and use of Statistics.
1.2. Statistical terms: populations, subpopulations, individuals and samples.
1.3. Types of variables.
2. Analysis of univariate data.
2.1. Representations and graphics of qualitative variables.
2.2. Representations and graphics of quantitative variables.
2.3. Numerical summaries.
3. Analysis of bivariate data.
3.1. Representations and graphics of qualitative and discrete data.
3.2. Representations and numerical summaries of quantitative data: covariance and correlation.
4.1. Random experiments, sample space, elemental and composite events.
4.2. Definition of Probability and Properties. Conditional Probability and the multiplication Law. Independence.
4.3. The law of total probability and Bayes theorem.
5. Probability models.
5.1. Random variables. Discrete random variables: The probability function and the distribution function. Mean and variance of a discrete random variable. Chebyshev's inequality.
5.2. Continuous random variables: The density function and the distribution function. Mean and variance of a continuous random variable.
5.3. Probability models. Discrete probability models: Bernoulli, Binomial and Poisson.
5.4. Continuous probability models: Uniform, Exponential and the normal distribution.
5.5. Central limit theorem.
6. Introduction to Statistical Inference.
6.1. Parameter point estimation.
6.2. Goodness-of-fit to a probability distribution. Graphical methods.
6.3. The sample mean distribution.
6.4. Confidence interval for the mean.