← Higher Math: Probability and Statistics

⇄ Sync
Length

Program
History and progress transfer
Choose a topic — problems will keep coming one after another for as long as you like

Theory of all steps of the program by blocks. Open a topic to read it.

How a session goes

A session is 10–90 minutes: a warm-up on what you've learned, new steps with short theory and problems, practice. Each problem gives two tries: 100 points on the first, 60 on the second; after the second mistake the correct answer is shown. You move on in the program if 70 % of the problems are solved.

Problems with numbers are generated anew every time a step is repeated. A fractional answer can be entered with a comma, a point or as a fraction: 0,5, 0.5, 1/2. In Practice any topic is available without a timer.

About the course

Conditional probability and Bayes, random variables, expectation and variance, binomial, Poisson, normal and other distributions, the LLN and CLT, estimates, confidence intervals, hypothesis testing and least-squares regression.

Course program: 30 lessons

Conditional probability and Bayes

  1. Conditional probability
  2. Law of total probability
  3. Bayes' formula
  4. Total probability and Bayes: more
  5. Checkpoint: conditional probability and Bayes

Discrete random variables

  1. Random variable and distribution table
  2. Expected value
  3. Variance and standard deviation
  4. Properties of M and D
  5. Checkpoint: discrete variables

Classic discrete distributions

  1. Binomial distribution
  2. Poisson distribution
  3. Geometric distribution
  4. Distributions: more
  5. Checkpoint: discrete distributions

Continuous random variables

  1. Density and distribution function
  2. Uniform distribution
  3. Exponential distribution
  4. Normal distribution and the three-sigma rule
  5. Continuous distributions: more
  6. Checkpoint: continuous variables

Dependence and limit theorems

  1. Covariance and correlation
  2. Law of large numbers and CLT
  3. Checkpoint: dependence and limit theorems

Mathematical statistics

  1. Samples and point estimates
  2. Confidence interval
  3. Hypothesis testing and p-value
  4. Linear regression: least squares
  5. Statistics: more
  6. Checkpoint: statistics