Syllabus Information

5.3. Syllabus

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Lesson 1: Discrete probability distributions.

Random variables. Discrete and continuous random variable. Probability distribution or mass function. Binomial, Hypergeometric and Poisson distributions.

Lesson 2: Continuous probability distributions.

Continuous random variable. Probability density function. Uniform and Exponential distributions. Normal distribution and related to normal distributions.

Lesson 3: Basic notions of sampling theory.

Sampling from a population. Sampling methods. Sampling distribution of statistics: Monte Carlo method. Asymptotic behavior of sampling moments. Sample-size determination.

Lesson 4: Point estimators and Interval estimation

Estimation. Building estimators: method of moments and maximum likelihood estimates. Properties of estimators.

Confidence interval. Methods of finding interval estimators. Confidence intervals for parameters of normal distribution. Some applications.

Lesson 5: Parametric hypotheses.

Basic concepts: Simple, compound, null and alternative hypotheses, significance level, power of a test. Tests of the mean and variance of a normal distribution, tests of the population proportion.

Lesson 6: Two-sample hypothesis tests.

Independent and dependent samples. Comparing proportions, means and variances: confidence intervals and tests of statistical hypotheses.