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The University of Texas at ArlingtonThe University of Texas at Arlington

College of Science


MATH 5312: Mathematical Statistics I


This course studies basic probability theory and various distributions. Properties of distributions are derived.


  • Sample space
  • Conditional probability
  • Independence
  • Random variables
  • Expected values
  • Mean, variance, covariance and correlation
  • Discrete distributions including binomial, negative binomial, hypergeometric, Poisson, etc
  • Continuous distributions including uniform, normal, gamma, exponential, t, χ2, F, etc
  • Moment generating functions
  • Distributions of functions of random variables
  • Central limit theorem
  • Limiting distributions


Bain, Lee J. and Engelhardt, Max (1992) Introduction to Probability and Mathematical Statistics, 2nd edition. Duxbury

Casella, George and Berger, Roger, L. (1990) Statistical Inference. Wadsworth