#### Abstract

In the first four chapters, we start with a review of classical probabilistic tools such as counting principles, probability concepts, definitions and theorems like conditional probability, Bayes’ rule, and independence of events.

In chapters 5-8 we introduce the notion of discrete and continuous random variables and their distributions. We present the most important examples like binomial, Poisson’s and normal distributions. By presenting numerous examples we show their applications.

The last chapters are devoted mainly to statistics. We give basic definitions and present the main ideas. Finally, we perform statistical tests and present the regression analysis method.

In the end, we show the application of Poisson distribution in reliability theory. A set of exercises for individual activities and learning is available.

#### Aim

To acquire skills in solving real time problems, especially these related to the sea and ships, by using probabilistic and statistical methods. It turns out that many problems in maritime domain are not deterministic and probabilistic tools are necessary.

#### Learning Outcomes

- Compute with classical definitions probability using basic counting principals
- Compute total and conditional probability
- Check the independence of events, and learn their applications
- Learn and apply discrete random variable distributions
- Learn the importance of normal distributions
- Perform statistical tests
- Calculate the linear regression
- Learn applications of probability and statistics in the maritime domain

#### Previous knowledge of mathematics

*Elementary mathematics, arithmetic, set theory, elements of Calculus, in particular definite integrals*

#### Relatedness with solving problems in the maritime field

The reason why we apply the probabilistic and statistical methods in maritime problems is that these problems are often unpredictable. The movement of ships in the sea is partially random. Partially means that, of course, we can steer the ship and respond to the actual situation, but in many extremely difficult situations it is not enough. We cannot predict many potentially risky conditions early enough. It is since we cannot describe the sea in the deterministic way. Sea waves are not deterministic. There is no “sea equations” that can describe how waves will behave at a place and time, even if we know the present situation there.

The second reason, why probability and statistics are so important in the maritime domain, is the reliability theory, which we apply to ship equipment. Ships spend usually long days in the sea, so we must be sure that all mechanical, electrical and electronic devices will be working properly.