Course Content

Probability Theory Update

1. Probability Basics

Set Theory Probability Experiment Statistical Independence

2. Statistical Dependence

Dependent Events Mutually Exclusive Events Addition Rule for Mutually Exclusive Events Addition Rule for Non-Mutually Exclusive Events Multiplication Rule for Independent Events Multiplication Rule for Dependent Events Conditional probability Bayes Rule

3. Learn Crucial Terms

Random Variable Discrete vs Continuous Random Variable Expected Value The Law of Large Numbers CMT

4. Probability Functions

Binomial Distribution Probability Mass Function (PMF) 1/2 Probability Mass Function (PMF) 2/2 Cumulative Distribution Function (CDF) 1/2 Cumulative Distribution Function (CDF) 2/2 Probability Density Function (PDF) 1/2 Probability Density Function (PDF) 2/2

5. Distributions

Poisson Distribution 1/3 Poisson Distribution 2/3 Poisson Distribution 3/3 Standard Normal Distribution (Gaussian distribution) 1/2

Standard Normal Distribution (Gaussian distribution) 1/2

What is it?

This is a continuous probability distribution for a real-valued random variable.

Key characteristics:

The mean value or expectation is equal to 0.
The standard deviation to 1.
The shape is bell-curved.
The distribution is symmetrical. Python realization:

We will generate standard normal distribution with the size 1000 and mean and standard deviation specific to the standard normal distribution. We use the function random.normal() from the numpy library with the parameters: loc is the mean value and scale is the standard deviation.

You can play with the distribution size and see how the distribution will be modified.


              123456789
            
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns

# Generate standard normal distribution with the size 1000
data = np.random.normal(loc = 0, scale = 1, size = 1000)

sns.histplot(data = data, kde = True)
plt.show()

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 5. Chapter 4

Standard Normal Distribution (Gaussian distribution) 1/2

What is it?

This is a continuous probability distribution for a real-valued random variable.

Key characteristics:

The mean value or expectation is equal to 0.
The standard deviation to 1.
The shape is bell-curved.
The distribution is symmetrical. Python realization:

You can play with the distribution size and see how the distribution will be modified.


              123456789
            
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns

# Generate standard normal distribution with the size 1000
data = np.random.normal(loc = 0, scale = 1, size = 1000)

sns.histplot(data = data, kde = True)
plt.show()

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 5. Chapter 4

Standard Normal Distribution (Gaussian distribution) 1/2

What is it?

This is a continuous probability distribution for a real-valued random variable.

Key characteristics:

The mean value or expectation is equal to 0.
The standard deviation to 1.
The shape is bell-curved.
The distribution is symmetrical. Python realization:

You can play with the distribution size and see how the distribution will be modified.


              123456789
            
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns

# Generate standard normal distribution with the size 1000
data = np.random.normal(loc = 0, scale = 1, size = 1000)

sns.histplot(data = data, kde = True)
plt.show()

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

Everything was clear?

Thanks for your feedback!

What is it?

This is a continuous probability distribution for a real-valued random variable.

Key characteristics:

The mean value or expectation is equal to 0.
The standard deviation to 1.
The shape is bell-curved.
The distribution is symmetrical. Python realization:

You can play with the distribution size and see how the distribution will be modified.


              123456789
            
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns

# Generate standard normal distribution with the size 1000
data = np.random.normal(loc = 0, scale = 1, size = 1000)

sns.histplot(data = data, kde = True)
plt.show()

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

Section 5. Chapter 4

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