Conteúdo do Curso

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()

Mude para o desktop para praticar no mundo realContinue de onde você está usando uma das opções abaixo

Tudo estava claro?

Obrigado pelo seu feedback!

Seção 5. Capítulo 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()

Mude para o desktop para praticar no mundo realContinue de onde você está usando uma das opções abaixo

Tudo estava claro?

Obrigado pelo seu feedback!

Seção 5. Capítulo 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()

Mude para o desktop para praticar no mundo realContinue de onde você está usando uma das opções abaixo

Tudo estava claro?

Obrigado pelo seu 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()

Mude para o desktop para praticar no mundo realContinue de onde você está usando uma das opções abaixo

Seção 5. Capítulo 4

Mude para o desktop para praticar no mundo realContinue de onde você está usando uma das opções abaixo