Syllabus

LEARNING OUTCOMES

After completing the course, the participant

• Can compute the expected value of a random number as an integral with respect to a probability measure
• Can compute probabilities related to independent random variables by using a product measure
• Recognizes different types of convergence of a random sequence
• Can explain how and when a random sum can be approximated by a Gaussian distribution
• Can represent conditional probabilities with respect to the information content of a sigma-algebra

Credits: 5

Schedule: 08.01.2024 - 19.02.2024

Teacher in charge (valid for whole curriculum period):

Teacher in charge (applies in this implementation): Lasse Leskelä

Contact information for the course (applies in this implementation):

Lecturer: Prof Lasse Leskelä

Teaching assistant: MSc Kalle Alaluusua

CEFR level (valid for whole curriculum period):

Language of instruction and studies (applies in this implementation):

Teaching language: English. Languages of study attainment: English

CONTENT, ASSESSMENT AND WORKLOAD

Content

• valid for whole curriculum period:

  - Random numbers, vectors, and sequences
  - Describing information using sigma-algebras
  - Integration with respect to a probability measure
  - Stochastic independence and product measure
  - Law of large numbers and the central limit theorem

Assessment Methods and Criteria

• valid for whole curriculum period:

  Weekly exercises and exam.

• applies in this implementation

  Evaluation

  The course grade g is determined by normalised exam points (e = E/E_max), normalised homework points (h = H/H_max), and normalised quiz points (q = Q/Q_max) according to 

             g = f( max( 1.00*e, 0.60*e + 0.30*h + 0.10*q ) )

  where f: [0,1] → {0,1,2,3,4,5} is a deterministic increasing function such that f(0.5) ≥ 1 and f(0.9) ≥ 5.

  See http://math.aalto.fi/exams for 

  • Individual study arrangements for exams (deadline to submit the form is 1 week before the exam, but the earlier the better) 
    
  • Exam rooms (announced 1 or 2 days before the exam)
  
  

Workload

• valid for whole curriculum period:

  2 x 2h lectures, 1 x 2h exercise sessions with weekly homeworks

DETAILS

Substitutes for Courses

• valid for whole curriculum period:

  Substitutes for Courses

Prerequisites

• valid for whole curriculum period:

  Prerequisites

FURTHER INFORMATION

Further Information

• valid for whole curriculum period:

  Teaching Language : English

  Teaching Period : 2022-2023 Spring III
  2023-2024 Spring III

  Enrollment :

  Registration takes place in Sisu (sisu.aalto.fi).

Description