Winter 2014/2015

Introduction to Statistics (with Matlab)

Lecture and Discussion

Exam: January 7th, 2015 (Wednesday), 11:05am-12:05pm in LG2A Room 2.20

The duration of the written examination will be 60 minutes.

You are allowed to use all your lecture notes, books and formularies. Calculators and other electronic devices are not permitted.

Content of the course

• 1. Week:

  Chapter 0: Introduction to Matlab (general introduction, complex numbers, vectors, matrices, plots, functions, Matlab as a programming language)

• 2. Week:

  Chapter 1: Introduction to statistics (introduction, data collection, descriptive statistics, inferential statistics, populations and samples)

  Chapter 2: Descriptive statistics (frequency table, line graph, bar graph, frequency polygon, relative frequency, pie chart, histogram, ogive, stem and leaf plot, sample mean, sample median, sample mode, sample variance, sample standard deviation, sample percentiles, box plot, and sample correlation coefficient)

• 3. Week:

  Chapter 3: Elements of probability (sample space, events, set theory, Venn diagrams, De Morgan's laws, axioms of probability, permutations, combinations, conditional probability, Bayes' formula, and independent events)

• 4. Week:

  Chapter 4: Random variables and expectation (random variables, discrete and continuous, cumulative distribution function, probability density/mass function, joint probability/mass function, independent random variables, expectation and its properties, moments, variance and its properties, covariance, correlation, and moment generating functions)

• 5. Week:

  Chapter 5: Special random variables (Bernoulli, binomial, Poisson, hypergeometric, uniform, normal, exponential, gamma, chi-square, student-t, F, and logistics)

• 6. Week:

  Chapter 6: Distributions of sampling statistics (random sample, population mean and variance, central limit theorem)

• 7. Week:

  Chapter 7: Parameter estimation (maximum likelihood estimators, interval estimates, one-sided upper/lower and two-sided confidence intervals, bias and unbiased estimator)

• 8. Week:

  Chapter 8: Hypothesis testing (significance levels, null hypothesis, type I and II error, power function, one-sided tests, t-test)

• 9. Week:

  Chapter 9: Regression (linear regression, least squares estimator, distribution of the estimators, statistical inference about the regression parameters, sample correlation coefficient, polynomial regression)

• 10. Week and 11. Week:

  Chapter 10: Introduction to time series (examples, objectives, some simple models, stationary models and the autocorrelation function, estimation and elimination of trend and seasonal components)