General

1. Syllabus
2. Generic Course Objectives
3. Classroom Behaviour

Topic 1. Review

1. Elementary set theory and logic.
2. Functions.
3. Summation notation.

Topic 2. Combinatorics

1. The definition of a finite set and its cardinality.
2. The number of words of a given length in a finite alphabet.
3. The elementary combinatorics of sets.
4. The inclusion-exclusion principle.
5. Pascals identity.
6. Permutations and combinations (subsets).
7. The binomial theorem.
8. Bipartitions of a finite set.
9. Counting functions of different kinds.

Topic 3. Probability Theory.

1. Discrete random experiments.
2. The sample space of a random experiment.
3. Events.
4. Random variables.
5. Relative frequency.
6. Probability.
7. Conditional Probability.
8. Independent events.
9. Bayes’ theorem.

Topic 4 Random Variabkles.

1. The distribution of a discrete random variable.
2. Distribution functions.
3. Density functions.
4. The mean and variance of a discrete random variable.
5. Chebyshev’s inequality.
6. Continuos random variables.
7. The law of large numbers.

Topic 5. Introduction to Statistics.

1. Independent samples.
2. Statistics and parameters.
3. Estimators.
4. Statistics which measure dispersion.
5. Transformations and changes of scale.
6. Stevens’ Classification
7. Standardization.

Topic 6. R programming.

1. Installation of R
2. Introduction to R

Topic 7. Probability distributions.

1. Bernoulli random variables.
2. The binomial distribution.
3. The Poisson distribution.
4. The sum of Poisson variables.
5. The multinomial distribution.
6. The normal distribution.
7. The normal approximation to the binomial distribution.
8. Distribution of the mean.
9. The central limit theorem.
10. Sampling from finite populations

Topic 8. Inferential statistics.

1. Estimation.
2. Confidence intervals.
3. Confidence intervals for the mean of a population.
4. Interpretation of confidence intervals
5. Behaviour of the error.

Topic 9. Hypothesis testing.

1. Comparison of the Neyman-Pearson and Fisher methodologies
2. Tipo I and II errors.
3. Power of a test. Power curves
4. Inferences concerning the mean.
5. Comparison of two means
   • The case of “large” samples.
   • The case of “small” samples from populations of known variances.
6. Comparison of two variances.
7. Inferences concerning the proportion.
8. Non parametric tests.
9. Tests for independence.

Topic 10. Simple Linear Regression.

1. Confidence intervals for the regression parameters.
2. Inferences concerning the regression parameters
3. Predictions
4. Confidence intervals for predictions.
5. The analysis of residuals.
   1. Heteroscedastic data.
   2. Outliers and remedial measures.
6. SAS general linear model procedure.
7. Introduction to the analysis of variance.

Sample Exams

• MATH 3026 Exam I
• MATH 3026 Exam II
• MATH 3026 Exam III
• MATH 3026 Exam IV

Exercises

• Descriptive Statistics
• Distrubution of the Mean
• Elementary Combinatorics
• Probability
• Density functions
• Binomial
• Probability Trees
• Independence
• The Normal Distribution
• Tests of Hypotheses
• SAS Exercises
• SAS Assignments 1991-1994
• Regression and Correlation
• Different Statistics

Related Notes

1. The Distribution of the Mean
2. Projection and Least Squares (Advanced version)
3. Linear Correlation
4. Some Important Density Functions
5. Selected Formulae
6. Elementary Combinatorial Formulae

Bibliography

1. Murray R Spiegel Schaum’s Outline of Statistics, McGraw-Hill.
2. Feller, Introduction to Probability Theory and its Applications (Vol. 1), Wiley.

Evaluation

Grade will be based upon 4 exams.