MATA2600 Basic course in probability (4 cr)

• 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.

• 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

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The concepts of number series and integral.

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