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MA 332
MA 332 -- Mathematical Probability and Statistics II
- Continuous Random Variables and Their Probability Distributions
- Uniform, normal and other continuous distributions
- Expected Value
- Moments and Moment-Generating Functions
- Tchebyshef's Theorem
- The normal approximation to the binomial distribution
- Multivariate Probability Distributions
- Marginal and conditional probability distributions
- Independent random variables
- Expected value of a function of random variables
- Covariance of two random variables
- The multinomial probability distribution
- Conditional expectations
- Hypothesis Testing
- Type I and Type II errors
- Tests about proportions, means, and differences of means
- Tests about a single variance and about two variances
- Sign Test for a paired experiment
- Runs Test: a test for randomness
- Likelihood Ratio Tests
- Properties of Point Estimators and Methods of Estimation
- Properties
- Common unbiased estimators
- Relative efficiency
- Method of moments
- Method of maximum likelihood
- Considerations in Designing Experiments
- Elements affecting the information in a sample
- Physical process of designing an experiment
- Random sampling and the completely randomized design
- Volume-increasing experimental designs
- Noise-reducing experimental designs
- Advanced Topics in Probability
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