Introduction to probability and statistics with applications, combinatorics, random variables, probability distributions (with emphasis to distributions used in hydrology), Bayesian inference, inferential statistics, estimation of parameters, hypothesis testing, and linear regression.
1. Basic descriptive statistics. Inferential statistics.
2. Probability-random events, definition of probability, condition probability, independence of random events.
3. Discrete random variables & distribution, expectation, variance, examples of discrete distributions.
4. Continuous random variables & density, distribution functions, quantiles, expectation, variance, examples of continuous distributions.
5. Normal distribution.
6. Log-normal distribution.
7. Two-dimensional distribution, marginal distribution, independence, correlation.
8. Central limit theorem. Distribution of mean.
9. Estimation of parameters. Properties of estimators. Confidence intervals.
10. Hypotheses testing. Principle of hypotheses testing. One and two-sample problems.
11. Linear regression. Method of least squares.
12 .Linear regression. Estimation of parameters. Prediction.
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