Overview
This is a course for the HSE students in DSBA stream, that introduces basic concepts of probability theory and statistics. The topics include the definitions of probability, central limit theorem, distributions of random variables, estimators, hypotheses testing and their applications. The course contains a variety of practical exercises with solutions and essential theory.
Materials
| Combinatorics. Basics of probability | π | ποΈ |
| Geometric probability. Conditional probability | π | ποΈ |
| Bayesβ theorem. Bernoulli scheme | π | ποΈ |
| Random variables. Expected value and variance | π | ποΈ |
| Joint distributions. Covariance and correlation | π | ποΈ |
| Conditional expectation. Continuous distributions | π | ποΈ |
| Quantile function. Normal distribution | π | ποΈ |
| Joint continuous distributions. Random variables transformations | π | ποΈ |
| Poisson process. Convolution and marginalization. Limit theorems | π | ποΈ |
| Auxiliary distributions. Law of large numbers. Sample mean | π | ποΈ |
| Sample variance. Sample proportion. Point estimators | π | ποΈ |
| Method of moments estimator. Ordinary least squares. Maximum likelihood estimator | π | ποΈ |
| Confidence intervals for mean and variance. Accuracy of estimation | π | ποΈ |
| Confidence intervals for proportions, difference of means and ratio of variances | π | ποΈ |
| Review. Sample correlation and Spearman's rank correlation coefficients. Confidence interval for correlation coefficient | π | ποΈ |
| Hypotheses testing. Type I and II errors. Power of the test | π | ποΈ |
| Hypotheses testing with z-scores and t-scores | π | |
| Hypotheses testing with chi2-scores and F-scores | π | |
| Hypotheses on correlation. chi2-tests | π | |
| One-way ANOVA. Two-way ANOVA | π | |
| ANOVA confidence intervals. Family-wise error rate | π | |
| Simple linear regression. Interval estimation in normal regression | π | |
| ANOVA in simple linear regression. Coefficient of determination | π | |
| Multiple variables linear regression. ANOVA in multiple variables linear regression. Adjusted coefficient of determination | π | |
| Module III review | π |
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