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

Binomial probability 2/2

Look at the code example of the binomial probability


              12345
            
# Import relevant library
from scipy.stats import binom
# Here, we simulate an experiment of tossing 5 coins three times
experiment = binom.rvs(p = 0.5, size = 5, n = 3)
print(experiment)

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.

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.

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

Everything was clear?

Section 1. Chapter 5

Binomial probability 2/2

Look at the code example of the binomial probability


              12345
            
# Import relevant library
from scipy.stats import binom
# Here, we simulate an experiment of tossing 5 coins three times
experiment = binom.rvs(p = 0.5, size = 5, n = 3)
print(experiment)

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.

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.

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

Everything was clear?

Section 1. Chapter 5

Binomial probability 2/2

Look at the code example of the binomial probability


              12345
            
# Import relevant library
from scipy.stats import binom
# Here, we simulate an experiment of tossing 5 coins three times
experiment = binom.rvs(p = 0.5, size = 5, n = 3)
print(experiment)

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.

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.

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

Everything was clear?

Look at the code example of the binomial probability


              12345
            
# Import relevant library
from scipy.stats import binom
# Here, we simulate an experiment of tossing 5 coins three times
experiment = binom.rvs(p = 0.5, size = 5, n = 3)
print(experiment)

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.

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

Section 1. Chapter 5

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