Probability Theory

Probability Theory

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1. Learn Basic Rules

It's time to dive deeper into the probability theory. Here we will learn basic formulas. The main idea of the section is to help to understand the term probability using real-life examples.

Random Variable

Bernoulli Trial 1/2

Bernoulli Trial 2/2

Binomial Probability 1/2

Binomial probability 2/2

2. Probabilities of Several Events

Here, we will get acquainted with the rules in probability theory. This section will be more complicated than the previous one. It will be attractive because we are going to work with the real challenges. But it should be noted that we learn some formulas.

Add Probabilities

Calculate Connected Probabilities

Multiply probabilities

Dependent probabilities

Law of Total Probability

3. Conducting Fascinating Experiments

Doing experiments is always funny, but here we will combine exciting tasks with programming learning. In this section, we will work with the binom object to conduct experiments in Python.

The First Experiment

The Second Experiment

The Third Experiment

Combine Your Knowledge

4. Discrete Distributions

Distribution is a key to probability learning, but don't be petrified by this term. This section provides you with real-life explanations and relevant formulas.

Discrete Uniform Distribution

Calculate Fascinating Probability

Bernoulli Distribution

Binomial Distribution

Poisson Distribution

5. Normal Distribution

The normal distribution is the most commonly used one. Here we will work with the distribution with the help of real-life challenges.

Normal Distribution

Course Content

Probability Theory

Probability Theory

1. Learn Basic Rules

Random Variable Bernoulli Trial 1/2 Bernoulli Trial 2/2 Binomial Probability 1/2 Binomial probability 2/2

2. Probabilities of Several Events

Add Probabilities Calculate Connected Probabilities Challenge Multiply probabilities Dependent probabilities Law of Total Probability Bayes Theorem Challenge

3. Conducting Fascinating Experiments

The First Experiment The Second Experiment The Third Experiment Combine Your Knowledge

4. Discrete Distributions

Discrete Uniform Distribution Calculate Fascinating Probability Bernoulli Distribution Binomial Distribution Challenge Poisson Distribution Challenge

5. Normal Distribution

Normal Distribution Challenge 1 Сhallenge 2

Random Variable

Have you ever wondered how often you usually use the word probability? It is time to dive deeper into this very familiar term!

Note
Please take a look at the simplest example: imagine that you toss a coin, it is always a 50% chance of getting head or tail. I mean that there are only two possible outcomes, and the probability for each case is 1/2 (1/2 equal to 50 %).

It is time to turn to the definition of the random variable and clarify how we received such numbers.

The random variable is a quantity that equals one and only one value depending on the result of testing result.

Let's assume that X is the random variable with several outcomes (getting head or tail); therefore, we can mark them as x1 and x2.

The formula for calculating the probability is the following:

Let's build a small table for the probability distribution of random variables:

I hope you're interested in learning probability theory now! Here, it would be best to memorize the formula written above and the definition of a random variable.

Indeed, each event can result either in success or failure. For instance, if you have a box with balls colored differently (red or green) and want to put a red one, your event has two outcomes: red ball or not a red ball.

The picture for the task:

Everything was clear?

Section 1. Chapter 1

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