MA 332

Mathematical Statistics

  1. Continuous Random Variables and Their Probability Distributions
    1. Uniform, normal and other continuous distributions
    2. Expected Value
    3. Moments and Moment-Generating Functions
    4. Tchebyshef's Theorem
    5. The normal approximation to the binomial distribution

  2. Multivariate Probability Distributions
    1. Marginal and conditional probability distributions
    2. Independent random variables
    3. Expected value of a function of random variables
    4. Covariance of two random variables
    5. The multinomial probability distribution
    6. Conditional expectations

  3. Hypothesis Testing
    1. Type I and Type II errors
    2. Tests about proportions, means, and differences of means
    3. Tests about a single variance and about two variances
    4. Sign Test for a paired experiment
    5. Runs Test: a test for randomness
    6. Likelihood Ratio Tests

  4. Properties of Point Estimators and Methods of Estimation
    1. Properties
    2. Common unbiased estimators
    3. Relative efficiency
    4. Method of moments
    5. Method of maximum likelihood

  5. Considerations in Designing Experiments
    1. Elements affecting the information in a sample
    2. Physical process of designing an experiment
    3. Random sampling and the completely randomized design
    4. Volume-increasing experimental designs
    5. Noise-reducing experimental designs

  6. Advanced Topics in Probability

Learning Outcome 1: The student will demonstrate an understanding of survey sampling and parameter estimation.

Learning Outcome 2: The student will demonstrate an understanding of hypothesis testing.

Learning Outcome 3: The student will demonstrate an understanding of descriptive statistics.