Probability Theory

Probability Theory

0%

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

Binomial probability 2/2

Look at the code example of the binomial probability

Explanation of the code above:

We need to import binom object from scipy.stats.
binom.rvs(p = 0.5, size = 5, n = 3) means that the probability of getting head is 50 %, p = 0.5; the size of sample in experiment is 5, size = 5; the number of trial is 3, n = 3.
In the output we can see an array with five results for each coin with the number of successful trials for each coin.

Task

Your task here is almost the same as in the previous chapter, play with one coin!

Imagine that here you have a coin with a general probability of 50%. Follow this algorithm:

Import the binom object from scipy.stats.
Conduct the experiment with binom object using rvs() function:
- Set p parameter equal to 0.5.
- Set size parameter equal to 1.
- Set n parameter equal to 5.

Please note, you can comment on the line where np.random.seed() was defined and "play with the coin" to receive various outputs.

Note
Explanation of the output : We were tossing one coin five times, and it only led to success in three cases.

Everything was clear?

Section 1. Chapter 5

toggle bottom row

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

Binomial probability 2/2

Look at the code example of the binomial probability

Explanation of the code above:

We need to import binom object from scipy.stats.
binom.rvs(p = 0.5, size = 5, n = 3) means that the probability of getting head is 50 %, p = 0.5; the size of sample in experiment is 5, size = 5; the number of trial is 3, n = 3.
In the output we can see an array with five results for each coin with the number of successful trials for each coin.

Task

Your task here is almost the same as in the previous chapter, play with one coin!

Imagine that here you have a coin with a general probability of 50%. Follow this algorithm:

Import the binom object from scipy.stats.
Conduct the experiment with binom object using rvs() function:
- Set p parameter equal to 0.5.
- Set size parameter equal to 1.
- Set n parameter equal to 5.

Please note, you can comment on the line where np.random.seed() was defined and "play with the coin" to receive various outputs.

Note
Explanation of the output : We were tossing one coin five times, and it only led to success in three cases.

Everything was clear?

Section 1. Chapter 5

toggle bottom row

some-alt