Course Content

Probability Theory Basics

1. Basic Concepts of Probability Theory

Stochastic Experiment and Random Event Probability and It's Properties Geometrical Probability Challenge: Solving the Task Using Geometric Probability Independence and Incompatibility of Random Events Conditional Probability

2. Probability of Complex Events

Inclusion-Exclusion Principle Challenge: Solving the Task Using Inclusion-Exclusion Principle The Multiplication Rule of Probability Law of Total Probability Bayes' Theorem Challenge: Solving the Task Using Bayes' Theorem

3. Commonly Used Discrete Distributions

Binomial Distribution Challenge: Solving Task Using Binomial Distribution Multinomial Distribution Geometric Distribution Poisson Distribution Challenge: Solving Task Using Poisson Distribution

4. Commonly Used Continuous Distributions

Continuous Uniform Distribution Exponential Distribution Challenge: Solving Task Using Exponential Distribution Gaussian Distribution Challenge: Solving Task Using Gaussian Distribution

5. Covariance and Correlation

What is Covariance?What is Correlation?Challenge: Solving the Task Using Correlation

Challenge: Solving the Task Using Bayes' Theorem

Task

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Imagine that we decided to conduct medical research.
You gathered data about two groups: 750 people with heart problems and 800 with chronic stomachache.
You know that 7% of interviewed from the first group have diabetes; meanwhile, 12% of respondents from the second group have diabetes too.
Calculate the probability that a randomly selected person with diabetes has a chronic stomachache.

We can use Bayes' theorem to calculate the corresponding probability.

Calculate the probability that a randomly selected person has a heart problem.
Calculate the probability that the randomly selected person has a stomachache.
Calculate the probability that you randomly select a person that has diabetes.

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Section 2. Chapter 6

Challenge: Solving the Task Using Bayes' Theorem

Task

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We can use Bayes' theorem to calculate the corresponding probability.

Calculate the probability that a randomly selected person has a heart problem.
Calculate the probability that the randomly selected person has a stomachache.
Calculate the probability that you randomly select a person that has diabetes.

Switch to desktop for real-world practiceContinue from where you are using one of the options below

Everything was clear?

Thanks for your feedback!

Section 2. Chapter 6

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