### 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. The student knows the three axioms of probability and associated

basic propositions and can use these to compute probabilities of events.

He understands the concept of independence and can compute conditional

probabilities (directly or with Bayes' rule).

2. The student can compute probability mass functions and density

functions, cumulative distributions, expectations and variances of

discrete and continuous random variables. He also knows important

discrete and continous probability distributions (Bernoulli, binomial,

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

and exponential distribution) and their properties and knows in which

context these distributions occur.distributions occur.

3. The student 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. The student can compute the probability distribution of a function of

a random variable or a random vector.

5. The student knows and can apply the central limit theorem.

### Course Content

We study experiments in which randomness plays a role. We first considerdiscrete probability experiments, that is 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 probabilities to events in a reasonable way, such that

the three axioms of probability are satisfied. We compute probabilities

in these situations and consider associated concepts like independence,

conditional probabilities, random variables and important discrete

probability distributions like 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 treat 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 treat

independence, conditional distributions and expectations, distributions

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

the Central limit theorem and the normal approximation to the Binomial

distribution.

### Teaching Methods

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

### Method of Assessment

Midterm (40%) and final exam (40%), biweekly quizzes (20%), see Canvasfor the details.

### Literature

Sheldon Ross, A first course in probability, 9th edition.### Target Audience

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

Calculus, Sets and Combinatorics (BA) or Basic Concepts in Mathematics(Mathematics). If you were not able to follow the course Basic Concepts

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

student, it is recommended to study the first chapter of Ross before the

start of the course.