ProbabilityLaajuus (3 ECTS)

Objective

After completing this course, the student will be familiar with the basic concepts and applications associated with probability and random variables. The student is able to construct and solve elementary stochastic models and interpret the results.

Content

1) Probability
2) Discrete random variables
3) Continuous random variables

Assessment criteria, satisfactory (1)

1) Probability
The student has got an idea of the notion of probability. The student is familiar with the set theoretic notation in probability theory. The student is able to compute elementary probabilities.
2) Discrete random variables
The student has got an idea of the notion of discrete random variable. The student is able to represent graphically a distribution and the cumulative distribution function. The student is able to calculate elementary probabilities as well as the expectation and the variance of a distribution.
3) Continuous random variables
The student has got an idea of the notion of continuous random variable. The student is able to determine probabilities from the cumulative distribution function. The student has got an idea of the expectation and the variance of a continuous distribution.

Assessment criteria, good (3)

1) Probability
The student is familiar with the notion of probability, its interpretations and the axiomatic basis of the probability theory. The student is able to solve basic problems involving combinatorics, conditional probability, independence, the total probability theorem and repeated experiments.
2) Discrete random variables
The student is familiar with the notions of discrete random variable, distribution, cumulative distribution function, expectation and variance. The student is able to solve basic problems involving discrete random variables. The student is familiar with the binomial distribution, geometric distribution and Poisson distribution and their parameters and applications. The student is able to utilize these distributions when modeling real world.
3) Continuous random variables
The student is familiar with the notions of continuous random variable, distribution, cumulative distribution function, expectation and variance. The student is able to solve basic problems involving continuous random variables. The student is familiar with the uniform distribution, exponential distribution and normal distribution and their parameters and applications. The student is able to utilize these distributions when modeling real world.

Assessment criteria, excellent (5)

1) Probability
The student has got exceptional skills in solving probability problems. The student is able to prove theorems from axioms.
2) Discrete random variables
The student has a profound understanding of the notion of discrete random variable and its potential in real-world modeling. The student has got exceptional skills in discrete stochastic modeling.
3) Continuous random variables
The student has a profound understanding of the notion of continuous random variable and its potential in real-world modeling. The student has got exceptional skills in continuous stochastic modeling.

Further information

Computer exercises will be included.