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 Task Using Exponential Distribution

Task

The average waiting time for a passing car on a rural road is 10 minutes. What is the probability of waiting more than 15 minutes for the next car if you have just seen another car?

We can solve this task using an exponential distribution. You have to:

Calculate the probability of waiting less than 15 minutes.
Calculate the probability of waiting for the car for more than 15 minutes, taking into account the fact that the sum of the probabilities of all elementary outcomes is always equal to 1.

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Section 4. Chapter 3

Challenge: Solving Task Using Exponential Distribution

Task

The average waiting time for a passing car on a rural road is 10 minutes. What is the probability of waiting more than 15 minutes for the next car if you have just seen another car?

We can solve this task using an exponential distribution. You have to:

Calculate the probability of waiting less than 15 minutes.
Calculate the probability of waiting for the car for more than 15 minutes, taking into account the fact that the sum of the probabilities of all elementary outcomes is always equal to 1.

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 4. Chapter 3

Challenge: Solving Task Using Exponential Distribution

Task

The average waiting time for a passing car on a rural road is 10 minutes. What is the probability of waiting more than 15 minutes for the next car if you have just seen another car?

We can solve this task using an exponential distribution. You have to:

Calculate the probability of waiting less than 15 minutes.
Calculate the probability of waiting for the car for more than 15 minutes, taking into account the fact that the sum of the probabilities of all elementary outcomes is always equal to 1.

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

Everything was clear?

Thanks for your feedback!

Task

The average waiting time for a passing car on a rural road is 10 minutes. What is the probability of waiting more than 15 minutes for the next car if you have just seen another car?

We can solve this task using an exponential distribution. You have to:

Calculate the probability of waiting less than 15 minutes.
Calculate the probability of waiting for the car for more than 15 minutes, taking into account the fact that the sum of the probabilities of all elementary outcomes is always equal to 1.

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

Section 4. Chapter 3

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