# MATA2600 Basic course in probability (4 cr)

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## Description

Combinatorics: product rule, permutation, variation and combination.

Probability: axioms and rules, conditional probability, independence of events, Bayes formula.

Discrete random variables: distributions, random vectors, joint distributions, marginal distributions, independence, conditional distribution, characteristics of distributions.

Geometric probability.

Continuous distributions: density function, expected value, variance, normal distribution.

## Learning outcomes

- knows how to use the product rule, permutation, variation and combination to calculate the number of elements in a set
- knows the axioms of probability
- can calculate the probabilities of the complement, intersection, union and difference of events using rules of probability
- understands what the conditional probability of an event means and can calculate it also using the Bayes formula
- understands what independence of events means and knows how to use it in calculating probabilities

- knows how to form the distribution of a random variable and its transformation, and calculate the expected value and variance using the distribution
- is able to form the joint distribution of several random variables and understands what it says about the probabilities of the different values of the random variables
- knows how to calculate the marginal distribution from the joint distribution and knows that it is the distribution of the corresponding individual random variable
- can determine from the joint distribution whether the random variables are independent
- knows what it means when random variables are correlated and what this means in terms of independence or dependence
- knows how to calculate conditional distributions from the joint distribution and understands what conditional distribution means

- understands how geometric probability is formed and is able to determine it for simple problems
- knows how to use the density function to represent the probability distribution and calculate the expected value and variance
- understands the connection between the density function and the cumulative distribution function
- knows how to calculate probabilities of normal distribution using the distribution function

## Additional information

Opintojaksoja TILA1200 Todennäköisyyslaskenta 1 sekä MATA2600 Todennäköisyysmatematiikka molempia ei voi sisällyttää opintokokonaisuuteen.

## Description of prerequisites

The concepts of number series and integral.

## Study materials

Ross, Sheldon M., A First Course in Probability (8th edition), sections 1.1-1.5, 2.1-2.5, 3.1-3.5, 4.1-4.9.1, 5.1-5.5, 6.1-6.4, 7.1-7.4

## Literature

- Ross, Sheldon M., A First Course in Probability, Pearson Prentice Hall cop. 2010. 8th ed
- Ross, Sheldon M. Introduction to Probability and Statistics for Engineers and Scientists. Elsevier, 2004.

## Completion methods

### Method 1

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### Method 2

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### Participation in teaching (4 cr)

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#### Teaching

##### 3/17–5/25/2025 Lectures

### Exam (4 cr)

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