PhD Qualifying Exam Information for Engineering Statistics

Materials Permitted:

  • Hard copy (typed or hand written) notes covering the topics below and created by the student taking the exam.
  • Calculator

Probability Theory

  • Probability Set Function
  • Conditional Probability and Independence
  • Random Variables, Common Distributions
  • Expectation (including Moment Generating Functions)
  • Function(s) of Random Variables • Important Inequalities
  • Convergence
  • Exponential Distribution Family

Statistics

  • Properties of a Random Sample
    • Asymptotic Properties of Sample Mean
    • Sampling from a Normal Distribution
    • Order Statistics
    • Sufficient and Complete Statistics
  • Point Estimation
    • Method of Moments
    • Maximum Likelihood Estimation
    • Bias, Efficiency and Consistency of Point Estimators
    • Best Minimum Variance Unbiased Estimator
    • Bayesian Estimator (including Markov Chain Monte Carlo - MCMC)
  • Hypothesis Testing I
    • Elements of a Statistical Test
    • Some Common Tests (concerning means, variances, etc.)
    • Goodness-of-Fit