Course Learning Outcomes:

1. Work with critical concepts, tools, techniques, and skills in computer programming, statistical inference/learning and machine learning.
2. Use visualization to understand data.
3. Work with the computational tools and practices for summary, analysis, and visualization of data.
4. Analyze real data sets and communicate their results.
5. Have a basic understanding of the implications and tools of data collection.

Course Learning Outcomes:

1. Have experience working with Bernoulli and binomial distributions, negative binomial and geometric distributions, hypergeometric distribution, Poisson distribution, the normal distribution, the central limit theorem.
2. Have experience working with discrete random variable, continuous random variables, expectation, moments, Chebyshev's theorem, moment-generating-functions.
3. Have experience working with sample spaces, events, probability of an event; review of set notation, counting rules and combinatorial methods, rules of probability conditional probability; independent events, Bayes' theorem.
4. Understand the fundamental concepts in probability with an emphasis on inquiry-based problem solving.

Course Learning Outcomes:

1. Calculate expected values.
2. Calculate probabilities of interest.
3. Understand and apply basic concepts of probability.
4. Understand and apply concepts of joint, marginal and conditional distributions.
5. Understand concepts of random variables and probability distributions.

Course Learning Outcomes:

1. Be able to find the distribution of functions of random variables, and understand how classical distributions such as t-distribution, F-distribution and χ2 distribution are defined.
2. Understand basic statistical estimation procedures, including maximum likelihood estimation and method of moments.
3. Understand the concept of hypothesis testing and be able to apply appropriate statistical tests for comparing means, proportions and variances.
4. Understand the concept of interval estimation and be able to find the confidence intervals of means, proportions and variances.
5. Understand the law of large numbers and the central limit theorem and how they are applied in the development of statistical theory.

Course Learning Outcomes:

1. Applying analysis of variance to understand the sources of uncertainty; applying least square criterion to build fitted models.
2. Conducting data analysis using linear regression models and reporting the analysis results.
3. Creating scatter plots, boxplots, pairwise plots to explore the data; analyzing data using linear regression models; obtaining least square estimates; comparing two different linear regression models; choosing significant variables; performing regression diagnostics for assessing the adequacy of models; drawing conclusions based on the analysis results.
4. Evaluating the appropriateness of using linear regression models in real applications.
5. Using built-in functions in R software to perform linear regression analysis.
6. Writing independent functions and codes in R to conduct linear regression analysis.

Course Learning Outcomes:

1. Apply appropriate methods for statistical analysis and interpret the output.
2. Apply common machine learning algorithms with real-world applications.
3. Import and tidy data for further analysis.
4. Visualize data and perform exploratory data analysis.
5. Understand the basics of numerical and Monte Carlo methods.
6. Understand the fundamental concepts in programming and R.

Course Learning Outcomes:

1. Computing an expectation using conditioning.
2. Computing an expectation using Markov Chain Monte Carlo.
3. Converting a process description into a Markov chain model.
4. Identifying the stationary distribution of Markov chains.
5. Proving results about Markov chains.
6. Understanding the mathematical structure of a Markov chain.

Course Learning Outcomes:

1. Demonstrate proficiency in finding the Fisher information contained in the data about unknown parameters.
2. Find Bayesian estimators for different functions of unknown parameters, under various loss functions.
3. Find the best unbiased estimators in the Hardy-Weinberg genetic equilibrium model.
4. Identify least informative prior distributions of unknown parameters and the resulting minimax admissible procedures.

Course Learning Outcomes:

1. Apply Markov Chain Monte Carlo for approximating the posterior distributions in Bayesian statistical Analysis.
2. Implement common algorithms in R for simulating random variables/vectors from standard and non-standard distributions.
3. Use standard Monte Carlo methods and importance sampling for approximating integrals, expectations and probabilities.
4. Understand common unsupervised learning methods including density estimation, clustering and dimension re-duction techniques.
5. Understand the EM algorithm and its implementation in estimation for mixture models and censored data.
6. Understand the use of spline and penalization methods in supervised learning.

Course Learning Outcomes:

1. Derive properties of distributions; finding optimal estimators and tests.
2. Develop a theoretical understanding of discrete and continuous random variables, distribution functions, sampling distributions, point estimation, interval estimation, hypothesis testing, large sample theory and basic Bayesian methods.
3. Prove Rao-Blackwell theorem, Lehmann-Scheffe theorem, Neyman-Pearson lemma.

Course Learning Outcomes:

1. Deal with deterministic temporal structure in the data collected.
2. Use time-series models to do forecasting
3. Work with probabilistic analysis of regular time-series data.
4. Work with time-series data collected at regular intervals over time, e.g., daily temperature.

Course Learning Outcomes:

1. Compute numerical implementation of the scoring method for finding the maximum likelihood estimates in the cases of real and vector parameters.
2. Compute numerical solution of equations and numerical maximization of expressions depending on a real parameter.
3. Handle numerically various Poisson regression and binomial logistic regression models.
4. Identify the best unbiased estimates for the unknown parameters of exponential families of distribution.

Course Learning Outcomes:

1. Be able to analyze the real data set with R software using appropriate models.
2. Be able to identify and classify data problems in survival analysis, define the appropriate survival function, distribution function, hazard function, and cumulative hazard function.
3. Understand and be able to compare survival functions of two or more populations.
4. Understand and be able to estimate survival functions using parametric, non-parametric, and semiparametric methods.