**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 |