Probability, Statistics and OptimizationLaajuus (5 cr)

Objective

The student learns fundamental mathematical concepts, principles, tools (including computing environments) and terminology of statistics, probability and optimization for professional studies.

Content

Theory of statistics and probability
- Numerical and graphical description of data
- Probability, probability rules and theorems, probability distribution
- Modeling, parameter estimation
- Model selection, decision theory
- Analysis task types

Optimization, differential calculus and numerical computation
- Objective function
- Critical points, extrema
- Types of optimization problems
- Limit, derivative, partial derivative, differentiation rules
- Iterative gradient-based optimization methods, derivative-free methods

Assessment criteria, satisfactory (1)

Assessment criteria - grade 1
The student knows the concepts of probability, statistics, and optimization and is able to solve basic problems.

Assessment criteria, good (3)

Assessment criteria - grade 3
The student understands the concepts of probability, statistics, and optimization and is able to solve varied problems related to applications of probability, statistics, and optimization.

Assessment criteria, excellent (5)

The student understands the concepts of probability, statistics, and optimization and is able to apply methods of probability, statistics, and optimization in solving and handling new types of problems.