Department of Industrial Engineering
4207 Bell Engineering Center
1 University of Arkansas
Fayetteville, AR 72701
Phone: (479) 575-3156
Fax: (479) 575-8431
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