1. Generating Functions (1.1 1. Moment generating functions, 1.2 2. Probability generating functions, 1.3 3. Compound random variables, 1.4 4. Cumulant generating functions)
2. Construction and estimation of statistical models (2.1 1. The main elements of classical inference, 2.2 2. Estimation, 2.3 3. Properties of estimators, 2.4 4. Method of moments for estimators, 2.5 5. Maximum likelihood estimates for estimators)
3. Confidence interval estimation (3.1 1. Pivotal quantities, 3.2 2. Sampling from a normal distribution, 3.3 3. Confidence intervals for means, variances and proportions, 3.4 4. Confidence intervals for binomial distribution, 3.5 5. Comparing two populations)
4. Hypothesis Testing (4.1 1. Hypotheses and test statistics, 4.2 2. p-value of a test, 4.3 3. Hypothesis tests for means and variances for single and two populations, 4.4 4. Hypothesis tests for proportions for single and two populations)
5. Relationships between two variables (5.1 1. Pearson's product moment correlation coefficient including hypothesis test, 5.2 2. Fitting the linear regression model using ordinary least squares; confidence intervals and tests of hypotheses for parameters, 5.3 3. Residuals, variability and assumptions)
By the end of the course, students should be able to do the following:
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SCQF Level: 8
Credits: 15