The ultimate objective of this course is to provide the student knowledge and understanding of the basic concepts and applications of the theory of probability and Statistical Inference required for the control and risk analysis in the areas of insurance and finance. Specific responsibilities: to acquire knowledge and understanding to: 1. Analyze data from one and two variables. 2. Explain concepts of probability and resolve problems of probability. 3. Use models of random variables, and unideminsionales bidimesionales. 4. Know and apply the Central Limit Theorem. 5. Explain the basic concepts of sampling. 6. Deduct point estimators for the mean, the variance and the proportion of a population. 7. Estimate using confidence intervals the mean, the variance and the proportion of a population. 8. Explain the basic concepts of hypothesis contrast. 9. Perform basic contrasts for one or two normal populations, binomial or Poisson. 10. Perform contrasts of goodness of fit. 11. Make contingency tables and apply contrasts of independence of two classification criteria. 12. Learn how to apply all the previous statistical methods with the help of statistical software. Transferable skills: 1. Capacity for synthesis and analysis. 2. Knowledge of the use of statistical software. 3. Resolution of problems. 4. Team work. 5. Critical reasoning. 6. Oral and written communication.

Topic 1: Introduction. Review of concepts. 1.1. Descriptive statistics. Correlation and linear regression. 1.2. Probability concepts. Random variables. Central Limit Theorem. Statistical dependence and independence. 1.3. Probability distributions useful in actuarial practice. Binomial, Negative Binomial, Geometric, Poisson, Pareto, Uniform, Normal, log-Normal, Student's t, Chi-square, Gamma, Exponential, Beta and Weibull distributions, among others. 1.4. Exercises and practical applications in R. Topic 2: Statistical inference and its actuarial and financial application. 2.1. Non-parametric estimation. Kernel estimation, adjustment and validation methods. 2.2. Parametric Estimation. Method of Moments, Maximum Likelihood and Percentile Matching method. Confidence Intervals and Hypothesis Tests. 2.3. Exercises and practical applications in R. Topic 3: Statistical techniques and their application in insurance. 3.1. Risk measures. 3.2. Calculation of probabilities. Simulation of scenarios. Cross-validation. 3.3. Aggregate models. 3.4. Optimisation algorithms. 3.5. Practical applications in R.

THEORY (4 ECTS): Theoretical classes with material of available support in the Web (collection guides / slides and exercises, basic bibliographical material and complementary material to study in depth those topics in which they are more interested). There will develop the fundamental theoretical and practical concepts of the subject that the pupil must acquire, and exercises will be solved on the part of the teacher, encouraging the active participation of the students in the resolution of the same ones (both of individual form and in team(equipment)). PRACTICES (2 ECTS): Classes of problem solving on the part of the pupils. Computer practices in computer rooms. Oral presentations and discussions.