Introduction to Probability and Statistics

Course Number: 
Hours - Lecture: 
Hours - Lab: 
Hours - Recitation: 
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Typical Scheduling: 
Every semester

This course is a problem oriented introduction to the basic concepts of probability and statistics, providing a foundation for applications and further study.


MATH 2401 or MATH 24X1 or MATH 2411 or MATH 2551 or MATH 2561 or MATH 2550 or MATH 2X51 or MATH 2605.

Course Text: 

At the level of Probability and Statistical Inference, Hogg and Tanis, 9th edition, Pearson

Topic Outline: 

Basic Principles Covered:

  • Multiplication principle, combinations, permutations
  • Inclusion-exclusion
  • Expected value, variance, standard deviation
  • Conditional probability, Bayes rule, partitions
  • Random variable, p.d.f., c.d.f., m.g.f.
  • Independence
  • Joint distributions, marginals, conditional expectations
  • Covariance, correlation
  • Transformations of a random variable
  • Central limit theorem, approximations
  • Basic distributions: uniform, binomial, multinomial, normal, exponential, Poisson, geometric, Gamma, Chi-squared, Student t, use of tables



  • Experiments, events, sets, probabilities, and random variables
  • Equally likely outcomes, counting techniques
  • Conditional probability, independence, Bayes' theorem
  • Expected values, mean, variance, binomial and geometric distributions
  • Poisson, moment generating functions
  • Continuous random variables, exponential, gamma, and normal; intuitive treatment of the Poisson process and development of the relationship with the gamma distributions
  • Uniform and simulation
  • Multivariate distributions, calculation of probability, covariance, correlation, marginals, conditions
  • Distributions of sums of random variables
  • Central limit theorem


  • Maximum likelihood, optimal, and unbiased estimators, examples
  • Univariate transformations using the chi square as an important example
  • Develop the idea of confidence intervals, confidence intervals for means with known variance in the normal case, large sample confidence intervals for means. Give the results of such a development for differences in the two-sample problem.
  • Confidence intervals for variances and ratios of variances and applied problems
  • Large sample confidence intervals for proportions, the one and two sample case, with examples and sample size considerations
  • Introduction to formal hypothesis testing, calculation of size and evaluation of the power function. One and two sample tests of hypotheses for normal means and variances. Chi-squared goodness of fit test.