Teaching GuideTerm 2019/202020/212018/192017/182016/172015/162014/152013/142012/132011/122010/112008/092009/10 Higher Polytechnic University College
 Grao en enxeñaría en Tecnoloxías Industriais Subjects ESTATÍSTICA Contents
 Topic Sub-topic The following topics develop the contents established in the tab of the Verification Memory that are: Statistics Introduction to Statistics Introduction Random phenomena. Statistical inference. Stages of a statistical investigation. Problems. 2. Exploratory data analysis. Descriptive statistics. Tabulation of a sample with repetitive data: frequency table. Histogram Cumulative diagram Tabulation of a sample with non-repetitive data: frequency table. Measures of central tendency. Measures of dispersion. Other measures of dispersion. Measures of form. Diagram of boxes and whiskers. Analysis of the stability of the relative frequencies. Problems. 3. Probability. Sample space. Operations with success. Counting techniques Fundamental properties of the frequencies. Axioms of the probabilities. Probability function. Properties deduced from the axioms. Definition of probability according to Laplace. Probability conditioned. Product theorem Total probability theorem. Bayes theorem. Dependence and independence of events. Problems. 4. Ramdom variables. Random variable. Discrete random variable: characteristics. Continuous random variable: characteristics. Tchebycheff's theorem. Characteristic function Transformation of random variables. Problems. 5. Discrete random variables and probability distributions. Introducción. Pruebas de Bernouilli. Distribución binomial. Distribución geométrica. Distribución hipergeométrica. Distribución de Poisson. Aproximación de distribuciones. Problemas. 6. Continous random variables and probability distributions. Introducción. Distribución uniforme. Distribuciones Erlang y gamma. Distribución exponencial. Distribución de Weibull. Distribución normal. Gráficos de probabilidad. Problemas. 7. Joint probability distributions. Distribuciones de probabilidad conjuntas. Función de distribución conjunta. Distribuciones marginales. Variable aleatoria bidimensional discreta. Variable aleatoria bidimensional continua. Variables aleatorias independientes. Variable aleatoria n dimensional. Esperanza matemática. Teoremas de adición. Transformación de variables aleatorias. Teorema central de límite. Problemas. 8. Statistical inference. Statistical sampling. Distributions associated with a sampling process. Distribution of the sample mean. The statistical variance sample. Chi-square distribution of Pearson. Simple random sampling of a normal distribution. Student's t distribution. Student's reason F distribution of Snedecor. Problems. 9. Point estimation of parameters. Estimation by points. Centered estimators. Consistent estimators Sufficiency. Criterion of Neyman-Fisher. Methods of obtaining estimators. Problems. 10. Statistical intervals for a single sample. Confidence intervals. Confidence interval for the mean of a normal population with known variance. Confidence interval for the mean of a normal population with unknown variance. Confidence interval for the variance of a normal population. Confidence interval for the proportion of a population. Problems. 11. Test of hypotheses for a single sample. Contrast of statistical hypothesis. Unilateral and bilateral contrasts. P values in contrast to hypotheses. Connection between hypothesis contrasts and confidence intervals. General procedure for hypothesis contrasts. Test of the mean of a normal population with known variance. Test of the mean of a normal population with unknown variance. Contrast of the variance and standard deviation of a normal distribution. Contrast of the proportion of a population. Contrast of goodness of fit. Contrast with contingency tables. Problems. 12. Regression. Association between random variables. Regression analysis. Quadratic minimum linear regression. Problems.
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