Course Content

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

Bernoulli Trial 2/2

It is time to connect your math knowledge with your programming skills. Look to this example:


              1234567
            
# Import relevant libraries 
import numpy as np
from scipy.stats import bernoulli

# Here, you simulate an experiment of tossing 5 coins
experiment = bernoulli.rvs(p = 0.5, size = 5)
print(experiment)

You can treat this function as an actual experiment; whenever you click the run button, the output is different.

Explanation of the code above:

You need to import bernoulli object from scipy.stats. With this object, we will conduct a probability experiment on a computer.
bernoulli.rvs(p = 0.5, size = 5) means that the probability of getting head is 50 %, p = 0.5, the sample size in experiment is 5, size = 5.
The output shows an array with five results for each coin 1 means success and 0 means failure.
[1 1 1 1 0] we had a successful result for 4 coins and failed for the last one.

Note
In this chapter and many other chapters, we will use the np.random.seed() function, do not be petrified it should be written to make your and my outputs equal. Do not change it.

Task

Your task is to play a little bit with the function. Imagine that you have an unbelievable successful coin and in 90% of cases tossing a coin you receive a head. Follow the algorithm to experiment:

Import the bernoulli object from scipy.stats.
Conduct the experiment with bernoulli object using .rvs() method.
- Set p parameter equal to 0.9.
- Set size parameter equal to 1.

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

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 1. Chapter 3

Bernoulli Trial 2/2

It is time to connect your math knowledge with your programming skills. Look to this example:


              1234567
            
# Import relevant libraries 
import numpy as np
from scipy.stats import bernoulli

# Here, you simulate an experiment of tossing 5 coins
experiment = bernoulli.rvs(p = 0.5, size = 5)
print(experiment)

You can treat this function as an actual experiment; whenever you click the run button, the output is different.

Explanation of the code above:

You need to import bernoulli object from scipy.stats. With this object, we will conduct a probability experiment on a computer.
bernoulli.rvs(p = 0.5, size = 5) means that the probability of getting head is 50 %, p = 0.5, the sample size in experiment is 5, size = 5.
The output shows an array with five results for each coin 1 means success and 0 means failure.
[1 1 1 1 0] we had a successful result for 4 coins and failed for the last one.

Note
In this chapter and many other chapters, we will use the np.random.seed() function, do not be petrified it should be written to make your and my outputs equal. Do not change it.

Task

Your task is to play a little bit with the function. Imagine that you have an unbelievable successful coin and in 90% of cases tossing a coin you receive a head. Follow the algorithm to experiment:

Import the bernoulli object from scipy.stats.
Conduct the experiment with bernoulli object using .rvs() method.
- Set p parameter equal to 0.9.
- Set size parameter equal to 1.

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

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 1. Chapter 3

Bernoulli Trial 2/2

It is time to connect your math knowledge with your programming skills. Look to this example:


              1234567
            
# Import relevant libraries 
import numpy as np
from scipy.stats import bernoulli

# Here, you simulate an experiment of tossing 5 coins
experiment = bernoulli.rvs(p = 0.5, size = 5)
print(experiment)

You can treat this function as an actual experiment; whenever you click the run button, the output is different.

Explanation of the code above:

You need to import bernoulli object from scipy.stats. With this object, we will conduct a probability experiment on a computer.
bernoulli.rvs(p = 0.5, size = 5) means that the probability of getting head is 50 %, p = 0.5, the sample size in experiment is 5, size = 5.
The output shows an array with five results for each coin 1 means success and 0 means failure.
[1 1 1 1 0] we had a successful result for 4 coins and failed for the last one.

Note
In this chapter and many other chapters, we will use the np.random.seed() function, do not be petrified it should be written to make your and my outputs equal. Do not change it.

Task

Your task is to play a little bit with the function. Imagine that you have an unbelievable successful coin and in 90% of cases tossing a coin you receive a head. Follow the algorithm to experiment:

Import the bernoulli object from scipy.stats.
Conduct the experiment with bernoulli object using .rvs() method.
- Set p parameter equal to 0.9.
- Set size parameter equal to 1.

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

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

Everything was clear?

Thanks for your feedback!

It is time to connect your math knowledge with your programming skills. Look to this example:


              1234567
            
# Import relevant libraries 
import numpy as np
from scipy.stats import bernoulli

# Here, you simulate an experiment of tossing 5 coins
experiment = bernoulli.rvs(p = 0.5, size = 5)
print(experiment)

You can treat this function as an actual experiment; whenever you click the run button, the output is different.

Explanation of the code above:

You need to import bernoulli object from scipy.stats. With this object, we will conduct a probability experiment on a computer.
bernoulli.rvs(p = 0.5, size = 5) means that the probability of getting head is 50 %, p = 0.5, the sample size in experiment is 5, size = 5.
The output shows an array with five results for each coin 1 means success and 0 means failure.
[1 1 1 1 0] we had a successful result for 4 coins and failed for the last one.

Note
In this chapter and many other chapters, we will use the np.random.seed() function, do not be petrified it should be written to make your and my outputs equal. Do not change it.

Task

Your task is to play a little bit with the function. Imagine that you have an unbelievable successful coin and in 90% of cases tossing a coin you receive a head. Follow the algorithm to experiment:

Import the bernoulli object from scipy.stats.
Conduct the experiment with bernoulli object using .rvs() method.
- Set p parameter equal to 0.9.
- Set size parameter equal to 1.

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

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

Section 1. Chapter 3

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