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Course Weekly Lecture Plan

Week Topic
1 1. Sets, set operations, definitions of probability, counting and classical definition applications, joint and conditional probability
2 2. Total probability, Bayes theorem, statistical independence, combined experiments, permutation, combination, sampling with and without replacement
3 3. Bernoulli trials, binomial law, approximations for binomial law. Random variable definition, types, distribution function
4 4. Density function, probability mass function, Uniform, Exponential, Laplacian, Gaussian, Bernoulli, Binomial, Poisson random variables.
5 5. Classwork
6 6. One function of one random variable. Expected value, expected value of a function of random variable.
7 7. Conditional distribution and density functions. Conditional expected value, moments, characteristic function.
8 8. Multiple random variables. Joint event, joint distribution and density functions. Marginal distribution and density functions, conditional distribution and density functions (condition 2. variable)
9 9. Correlation, covariance, correlation coefficient, linear independence.
10 10. Classwork
11 11. Sampling experiment, population and sample. sampling statistics, point estimation of parameters. Unbiased and minimum variance estimators.
12 12. Sampling distribution. confidence intervals (one or two sided t or z)
13 13. p values and Hypothesis testing
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