Universitat Politècnica de Catalunya · BarcelonaTech

Statistics (2500215) – Course 2024/25 PDF

Contents

Probability model. Sample space. Events. Set diagrams. Law of total probability. Uniform probability in finite spaces. Permutations. Combinations. Conditional probability. Bayes Theorem. Independence between events. Probability interpretation. Relative frequency. Uncertainty measure. Probability problems.

Dedication

4h Large group + 4h Medium group + 12h Self Study
Total: 20h

Random variable. Distribution. Cumulative distribution function. Quantile function. Median. Discrete random variable. Continuous random variable. Probability density function. Parametric distributions, discrete and continuous distributions. Transformation of random variables. Bivariate distributions. Joint and marginal distributions. Conditional distributions. Mixture distributions. Independence between random variables. Stochastic process. Markov model. Poisson process. Hope. Variance. Standard deviation. Covariance. Correlation. Chebychev inequality. Probability distribution problems.

Dedication

6h Large group + 6h Medium group + 18h Self Study
Total: 30h

Sample. Statisticians. Location. Dispersion. Symmetry. Order. Histograms. Box plots. Cumulative sampling distribution. Q-Q plot. Exploratory data analysis.

Dedication

2h Large group + 2h Medium group + 6h Self Study
Total: 10h

Law of large numbers. Central limit theorem. Fisher–Tippett theorem. Properties of the estimators. Bias. Consistency. Minimum variance. Estimation by the method of moments. Properties. Improvements. Likelihood function. Maximum plausible estimate. Invariance principle. Asymptotic behavior. Estimation of confidence intervals (using normal distribution, t, chi2). Estimation of prediction intervals. Bayes estimation. Uniform a priori distribution. Credibility intervals. Conjugate distributions. Problems on parameter estimation.

Dedication

8h Large group + 8h Medium group + 24h Self Study
Total: 40h

Definition. Type I and II errors. Power. p-value. Parametric tests. Tests on mean and variance of normal populations. Likelihood ratio test. Non-parametric and goodness-of-fit tests. Sample size selection. Problems on hypothesis tests

Dedication

4h Large group + 4h Medium group + 12h Self Study
Total: 20h

Simple linear regression. Multiple linear regression. Categorical variables. Normal regression model. Coefficient of determination. ANOVA. Influence measures. Outliers Linear regression problems.

Dedication

6h Large group + 6h Medium group + 18h Self Study
Total: 30h