Applied Probability and Statistics

Summarizing quantitative data.

Measuring center in quantitative data : Summarizing quantitative data More on mean and median : Summarizing quantitative data Interquartile range IQR : Summarizing quantitative data Variance and standard deviation of a population : Summarizing quantitative data. Variance and standard deviation of a sample : Summarizing quantitative data More on standard deviation : Summarizing quantitative data Box and whisker plots : Summarizing quantitative data Other measures of spread : Summarizing quantitative data.

Modeling data distributions. Percentiles : Modeling data distributions Z-scores : Modeling data distributions Effects of linear transformations : Modeling data distributions.

Journal of Applied Probability and Statistics

Density curves : Modeling data distributions Normal distributions and the empirical rule : Modeling data distributions Normal distribution calculations : Modeling data distributions More on normal distributions : Modeling data distributions. Exploring bivariate numerical data. Introduction to scatterplots : Exploring bivariate numerical data Correlation coefficients : Exploring bivariate numerical data Introduction to trend lines : Exploring bivariate numerical data. Least-squares regression equations : Exploring bivariate numerical data Assessing the fit in least-squares regression : Exploring bivariate numerical data More on regression : Exploring bivariate numerical data.

Study design.

Statistical questions : Study design Sampling and observational studies : Study design Sampling methods : Study design. Types of studies experimental vs. Basic theoretical probability : Probability Probability using sample spaces : Probability Basic set operations : Probability Experimental probability : Probability.

• Department of Statistics and Applied Probability - UC Santa Barbara?

Randomness, probability, and simulation : Probability Addition rule : Probability Multiplication rule for independent events : Probability Multiplication rule for dependent events : Probability Conditional probability and independence : Probability. Counting, permutations, and combinations.

Counting principle and factorial : Counting, permutations, and combinations Permutations : Counting, permutations, and combinations Combinations : Counting, permutations, and combinations. Combinatorics and probability : Counting, permutations, and combinations. Random variables.

Statistics and applied probability

Discrete random variables : Random variables Continuous random variables : Random variables Transforming random variables : Random variables Combining random variables : Random variables. Binomial random variables : Random variables Binomial mean and standard deviation formulas : Random variables Geometric random variables : Random variables More on expected value : Random variables Poisson distribution : Random variables. Sampling distributions.

What is a sampling distribution?

In this Section

For an appropriate approach to the solution of these challenges a multitude of statistical techniques are to be mastered by today's scientists - regression for correlated data. The courses of the minor degree program in Applied Probability and Statistics will not treat all of these methods in detail but provide the participants nevertheless with a solid basis in probability and statistics. The minor degree program is attractive for all students interested in stochastic methods and modeling. A minor degree program in Applied Probability and Statistics provides students with an enhanced background in probability and statistics and a practical training in many fundamental and modern methods of applied probability and statistics.

Classes are interactive and the methodology is illustrated using the free programming language R. Graduates of the minor degree program are able to.

Special Volumes

Those are supplemented with elective modules for 10 ECTS credits. Elective modules can be chosen from all modules containing quantitative, program relevant subjects conditional on the approval of the program coordinator. It is recommended to establish a study plan with the program coordinator.

A minor in Applied Probability and Statistics can not be combined with a major in Mathematics or Biostatistics.