503 STAT_Probability and Mathematical Statistics

 

-Introduction and some simple concepts.

-Measures of location (Central tendency measures) and measures of dispersion (Measures of variability.

- Sample space, events counting sample points (combinations only)

- Probability of an event, additive rules.

- Conditional Probability, Multiplication Rule.

- Independent random events

- Random Variables (R.V.), Discrete Probability distributions

- Continuous Probability distributions, Chapter Review.

- Moments of a Random Variable, Mean of a linear combinations of Random Variables.

- Chebychev’s Inequality.

-Discrete Uniform distribution. Binomial distribution

- Hyper geometric distribution. Poisson distribution

- Normal distribution. Areas under the standard normal curve

- Applications of the normal distribution

- Random Sampling, Some important statistics, Sampling distributions

- Sampling distribution of the mean from normal populations, t-distribution

- Statistical Inference, Classical estimation methods, Estimation of the mean

- Standard error of a point estimate, estimating the difference between two means

- Estimating a proportion

- Estimating the difference between two proportions

- Testing a statistical hypothesis, One- and Two-tail tests, Types of errors

- Testing means with known population variance, Relation to confidence intervals

- Testing means with unknown population variance, two sample testing, paired comparison

- Testing simple proportion and two proportions

- Simple linear regression and multiple regression, correlation and its applications

- ANOVA one and two ways and its applications

-Principal component analysis, clustering technique