# MAT-01566 Mathematics 5, 5 cr

#### Person responsible

Henri Hansen

#### Lessons

Implementation | Period | Person responsible | Requirements |

MAT-01566 2019-01 | 4 |
Henri Hansen |
Final Exam and weekly exercises |

#### Learning Outcomes

In this course, the students learn the basic concepts of probabilities, random variables and random vectors. The students learn to compute discrete and continuous probabilities and expectation values such as variances and correlations. The students also learn to apply the probability calculus to practical problems. The students learn how to justify their claims using mathematical methods and to present their solutions orally as well as in written form.

#### Content

Content |
Core content |
Complementary knowledge |
Specialist knowledge |

1. |
Basic Notions of Probability Theory: Probability and Expectation, Conditional Probability, Total probability and Independence | Bayesian probability and Combinatorial analysis. | |

2. |
Random Variables: The Probability Mass and Density Functions, Important Discrete Random Variables, Important Continuous Random Variables and Expectation and Variance | Moment Generating Function | |

3. |
Random Vectors: Discrete and Continuous Random Vectors, Covariance and Correlation, Multinormal Distribution | Transformations of Random Vectors | |

4. |
Sampling distributions and statistical inference: Statistics and sampling distribution, The Central Limit Theorem, prediction intervals, test of statistical hypotheses |

#### Instructions for students on how to achieve the learning outcomes

The grade of the course is based on the final exam and exercises.

#### Assessment scale:

Numerical evaluation scale (0-5)

#### Partial passing:

#### Prerequisites

Course | Mandatory/Advisable | Description |

MAT-01366 Mathematics 3 | Mandatory |

#### Correspondence of content

Course | Corresponds course | Description |

MAT-01566 Mathematics 5, 5 cr | MAT-01560 Mathematics 5, 5 cr |