Statistics 2

This half course requires the student to develop the concepts introduced in Statistics 1 of measurement and hypothesis testing.


  • Set theory: the basics Axiomatic definition of probability
  • Classical probability and counting rules
  • Conditional probability and Bayes’ theorem.

Random variables:

  • Discrete random variables
  • Continuous random variables.

Common distributions of random variables:

  • Common discrete distributions
  • Common continuous distributions.

Multivariate random variables:

  • Joint probability functions
  • Conditional distributions
  • Covariance and correlation
  • Independent random variables
  • Sums and products of random variables.
  • Sampling distributions of statistics: Random samples
  • Statistics and their sampling distributions


Sampling distribution of a statistic

  • Sample mean from a normal population
  • The central limit theorem Some common sampling distributions
  • Prelude to statistical inference.

Point estimation:

  • Estimation criteria: bias, variance and mean squared error
  • Method of moments estimation
  • Least squares estimation
  • Maximum likelihood estimation.

Interval estimation:

  • Interval estimation for means of normal distributions
  • Use of the chi-squared distribution
  • Confidence intervals for normal variances.

Hypothesis testing:

  • Setting p-value, significance level, test statistic t tests
  • General approach to statistical tests
  • Two type of error
  • Tests for normal variances
  • Comparing two normal means with paired observations
  • Comparing two normal means
  • Tests for correlation coefficients
  • Tests for the ratio of two normal variances

Analysis of variance:

  • One-way analysis of variance
  • Two-way analysis of variance.

Linear regression:

  • Simple linear regression Inference for parameters in normal regression models;
  • Regression ANOVA;
  • Confidence intervals for E(y);
  • Prediction intervals for y;
  • Multiple linear regression models

If you complete the course successfully, you should be able to:

  • Apply and be competent users of standard statistical operators and be able to recall a variety of well-known distributions and their respective moments
  • Explain the fundamentals of statistical inference and apply these principles to justify the use of an appropriate model and perform tests in a number of different settings
  • Demonstrate understanding that statistical techniques are based on assumptions and the plausibility of such assumptions must be investigated when analysing real problems.
  • Newbold, P., W. Carlson and B. Thorne. Statistics for Business and Economics. London: Pearson.

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