### General Information

Course Code | X_400622 |
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Credits | 6 EC |

Period | P4+5 |

Course Level | 200 |

Language of Tuition | English |

Faculty | Faculty of Science |

Course Coordinator | dr. C.M. Quant |

Examiner | dr. C.M. Quant |

Teaching Staff |
dr. C.M. Quant |

### Practical Information

You need to register for this course yourself

Last-minute registration is available for this course.

Teaching Methods | Seminar, Lecture |
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Target audiences

This course is also available as:

### Course Objective

After this course:1. Students know the three axioms of probability and associated

basic propositions and are able to use these to compute probabilities of

events.

They understand the concept of independence and can compute conditional

probabilities (directly or with Bayes' rule).

2. Students can compute probability mass functions and density

functions, cumulative distributions, expectations and variances of

discrete and continuous random variables. They also know important

discrete and continous probability distributions (Bernoulli, binomial,

Poisson, geometric, negative bionomial, hyper geometric, uniform, normal

and exponential distribution) and their properties and know in which

context these distributions occur.

3. Students can work with jointly distributed random variables. He

can compute probabilities, use the concept of independence in this

context, compute marginal distributions, conditional distributions,

(conditional) expectations, covariances and correlations.

4. Students can compute the probability distribution of a function of

a random variable or a random vector.

5. Students know and can apply the central limit theorem.

### Course Content

We study experiments in which randomness plays a role. We first considerdiscrete probability experiments: experiments with a countable

number of possible outcomes. You can think of tossing dice, shuffling a

deck of cards, flipping coins etc. The possible outcomes form a set,

the so called sample space. Every subset of this sample space is an

event. We assign reasonable probabilities to events, such that

the three axioms of probability are satisfied. We compute probabilities

in these situations and consider associated concepts such as

independence,

conditional probabilities, random variables and important discrete

probability distributions e.g. the Bernoulli, Binomial, geometric,

hypergeometric, negative Binomial and Poisson distribution.

We then consider experiments with an uncountable number of possible

outcomes and continuous random variables. We consider a number of

well-known continuous distributions: the uniform, exponential, normal

and exponential distributions. We study joint distributions of several

(discrete or continuous) random variables. In this context we deal with

independence, conditional distributions and expectations, distributions

and expectations of functions of random vectors and covariance. We study

the Central limit theorem and normal approximations to Binomial

distributions.

### Teaching Methods

lectures (4 hours per week) and tutorials (2 hours per week). There willbe 4 short tests during the tutorials.

### Method of Assessment

Midterm exam (40%), final exam (40%) and short tests (20%), see Canvasfor the details.

### Literature

Anderson, D.F, Seppäläinen, T, and Valkó, B, Introduction toProbability, Cambridge University Press, 2018.

### Target Audience

Mathematics and BA, year 1 and premaster Mathematics### Recommended background knowledge

-First year calculus courses for BA or Mathematics. Mathematics studentshave their second Calculus course simultaneously with Probability

Theory.

-Sets and Combinatorics (BA) or Basic Concepts in Mathematics

(Mathematics). If you were unable to take the course Basic Concepts

in Mathematics or Sets and Combinatorics, e.g. because you are a part

time

student, it is recommended that you study Appendix B and C of the book

before the

start of the course.