MOL-003 · Introduction and statistical methods Sample material

Elements of probability theory

The mathematical toolkit of statistical physics: random events, probability and its properties, the distribution function, mean value and variance, macro- and microstates of a system, the binomial, Poisson and Gaussian distributions.

Estimated time: 3 h 3 activities

Learning objective

Learn the concepts of a random event, relative frequency and probability, and the addition and multiplication rules.
Learn to work with discrete and continuous distribution functions and to calculate the mean and variance.
Understand the macrostate, microstate and statistical weight of a system.
Know the binomial, Poisson and Gaussian distributions and the conditions for their use.

Expected outcomes

Calculates the probabilities of compound events with the addition and multiplication rules.
Finds the mean, variance and standard deviation from a given distribution.
Calculates the number of microstates and the probability of a macrostate for molecules distributed between parts of a vessel.
Chooses and applies the binomial, Poisson or Gaussian distribution according to the problem.

Interactive modelGalton board: random processes and the Gaussian distribution

Activities

Lecture
Lecture · 1 h 20 min · required
Problem solving on the topic "Elements of probability theory"
Practice · 1 h 20 min · required
Final test
Test · 20 min · required · pass ≥ 70%

Completion conditions

  • Lecture
  • Problem solving on the topic "Elements of probability theory"
  • Final test — at least 70%