Math 3026 Statistics with Computers

2011-2012– Semester I

Miscellaneous Notes

Sample Exams

Exercises

Catalog Description

Math 3026 Statistics with Computers Three credits. Five hours of lecture per week. Prerequisite: MATH 3151.

Elementary combinatorics. Probability theory. Descriptive statistics. Random variables. Discrete and continuous sampling distributions. Estimation. Hypothesis testing. Correlation and regression. Scientific programming. Statistical computer packages. Computer simulations of random experiments. The student will carry out programming projects in which the concepts of the course are implemented.

Syllabus and Class Notes

  1. Review.
    1. Elementary set theory and logic.
    2. Functions.
    3. Summation notation.
  2. Counting
    1. The definition of a finite set and its cardinality.
    2. The cartesian product and its cardinality.
    3. The number of words of a given length in a finite alphabet.
    4. The disjoint union of sets and its cardinality.
    5. The cardinality of the union of two sets.
    6. The inclusion-exclusion principle.
    7. The number of subsets of a finite set.
    8. The number of subsets of a given size in a finite set.
    9. Pascals identity.
    10. The binomial theorem.
    11. The number of bipartitions of a finite set.
    12. The number of permutations.
    13. The number of bijections between finite sets.
    14. The number of functions with finite domain and codomain.
    15. The number of injective functions with finite domain and codomain.
  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.
  4. Random variables.
    1. Discrete random variables.
    2. The distribution of a discrete random variable.
    3. Distribution functions.
    4. Density functions.
    5. The mean and variance of a discrete random variable.
    6. Chebyshev’s inequality.
    7. Continuos random variables.
    8. The law of large numbers.
  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.
  6. R programming.
    1. Installation of R
    2. Introduction to R
  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
  8. Inferential statistics.
    1. Estimation.
      1. Confidence intervals.
      2. Confidence intervals for the mean of a population.
      3. Interpretation of confidence intervals
      4. Behaviour of the error.
  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
      1. The case of “large” samples.
      2. 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.
  10. Analysis of bivariate data.
  11. Simple Linear Regression.
    1. Simple linear regression.
    2. Confidence intervals for the regression parameters.
    3. Inferences concerning the regression parameters
    4. Predictions
    5. Confidence intervals for predictions.
    6. The analysis of residuals.
      1. Heteroscedastic data.
      2. Outliers and remedial measures.
    7. SAS general linear model procedure.
  12. Introduction to the analysis of variance.

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.