Probability Theory
Description
The course Probability Theory is designed to familiarize students with the basic concepts of probability theory: random events, classical and statistical definitions of probabilities, addition and multiplication theorems of probabilities and their corollaries, repeated trials, discrete and continuous random variables, numerical characteristics of random variables. You will study the normal distribution in detail and at the end of the course you will get acquainted with some applications of the Monte Carlo method.
Each section of the course contains brief theoretical information and self-study tasks.
Knowledge requirements: completion of the course Welcome to Engee.
Total course time: ~4 hours.
Course program
Basic concepts of probability theory
The types of random events, classical and statistical definitions of probabilities, properties of probability, basic formulas of combinatorics and calculation of probabilities with their help are studied.
The addition and multiplication theorems of probabilities. Corollaries
The addition theorem of probabilities, the multiplication theorem of probabilities, the concept of independent events, the probability of occurrence of at least one event, the law of total probability and the Bayes' theorem are studied.
Repeated trials
Bernoulli’s formula, the local and integral De Moivre–Laplace theorem, and Poisson’s formula are studied.
Discrete random variables
The probability distribution of a discrete random variable, the binomial distribution, the Poisson distribution, the simple process, the geometric distribution, the numerical characteristics of discrete random variables (expected value, variance and standard deviation) are studied.
Continuous random variables
The cumulative distribution function, the probability density function and numerical characteristics of continuous random variables, uniform and exponential distributions are studied.
Normal distribution
The normal distribution, that a normal random variable falls within a given interval, the probability of a given deviation, the three-sigma rule, the central limit theorem, the skewness and kurtosis, and the chi-squared distribution are studied.
Monte Carlo method
Basic information is given about the essence of the Monte Carlo method, its errors, the generation of random numbers in Engee, examples of the application of the Monte Carlo method (calculation of the value of the number π, calculation of definite integrals, one-dimensional and two-dimensional random walks).