Зміст курсу

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

Random Variable

Random event:

A random event is an event whose outcome can not be predicted. Rolling a die or tossing a coin can be examples.

Random variable:

A random variable is a variable whose value is we don't know.

A random variable is used to quantify the output of the random event. We can define a random variable as s capital letter; let it be X in our example.

Example:

We were rolling a die two times and received numbers 3 and 5; so, we can say that a random variable is X = 3 + 5 =8.

Simulating a random variable with Python:

To simulate an experiment in Python we will use the function from the NumPy library: .choice(values, size = size, replace = True)

values - a list of possible outcomes of the event.
size - the number of times we repeat the experiment.
replace = True - it can be equal to False, but in this course, we will not change this parameter.

The experiment of rolling a six-sided die five times.


              1234567891011
            
import numpy as np


experiment = np.random.choice(range(1,7), size = 5, replace = True)

random_value = sum(experiment)


print("The outcomes of the experiment are:", experiment)

print("The Random value is equal to:", random_value)

Перейдіть на комп'ютер для реальної практикиПродовжуйте з того місця, де ви зупинились, використовуючи один з наведених нижче варіантів

Все було зрозуміло?

Секція 3. Розділ 1

Random Variable

Random event:

A random event is an event whose outcome can not be predicted. Rolling a die or tossing a coin can be examples.

Random variable:

A random variable is a variable whose value is we don't know.

A random variable is used to quantify the output of the random event. We can define a random variable as s capital letter; let it be X in our example.

Example:

We were rolling a die two times and received numbers 3 and 5; so, we can say that a random variable is X = 3 + 5 =8.

Simulating a random variable with Python:

To simulate an experiment in Python we will use the function from the NumPy library: .choice(values, size = size, replace = True)

values - a list of possible outcomes of the event.
size - the number of times we repeat the experiment.
replace = True - it can be equal to False, but in this course, we will not change this parameter.

The experiment of rolling a six-sided die five times.


              1234567891011
            
import numpy as np


experiment = np.random.choice(range(1,7), size = 5, replace = True)

random_value = sum(experiment)


print("The outcomes of the experiment are:", experiment)

print("The Random value is equal to:", random_value)

Все було зрозуміло?

Секція 3. Розділ 1

Random Variable

Random event:

A random event is an event whose outcome can not be predicted. Rolling a die or tossing a coin can be examples.

Random variable:

A random variable is a variable whose value is we don't know.

A random variable is used to quantify the output of the random event. We can define a random variable as s capital letter; let it be X in our example.

Example:

We were rolling a die two times and received numbers 3 and 5; so, we can say that a random variable is X = 3 + 5 =8.

Simulating a random variable with Python:

To simulate an experiment in Python we will use the function from the NumPy library: .choice(values, size = size, replace = True)

values - a list of possible outcomes of the event.
size - the number of times we repeat the experiment.
replace = True - it can be equal to False, but in this course, we will not change this parameter.

The experiment of rolling a six-sided die five times.


              1234567891011
            
import numpy as np


experiment = np.random.choice(range(1,7), size = 5, replace = True)

random_value = sum(experiment)


print("The outcomes of the experiment are:", experiment)

print("The Random value is equal to:", random_value)

Все було зрозуміло?

Random event:

A random event is an event whose outcome can not be predicted. Rolling a die or tossing a coin can be examples.

Random variable:

A random variable is a variable whose value is we don't know.

A random variable is used to quantify the output of the random event. We can define a random variable as s capital letter; let it be X in our example.

Example:

We were rolling a die two times and received numbers 3 and 5; so, we can say that a random variable is X = 3 + 5 =8.

Simulating a random variable with Python:

To simulate an experiment in Python we will use the function from the NumPy library: .choice(values, size = size, replace = True)

values - a list of possible outcomes of the event.
size - the number of times we repeat the experiment.
replace = True - it can be equal to False, but in this course, we will not change this parameter.

The experiment of rolling a six-sided die five times.


              1234567891011
            
import numpy as np


experiment = np.random.choice(range(1,7), size = 5, replace = True)

random_value = sum(experiment)


print("The outcomes of the experiment are:", experiment)

print("The Random value is equal to:", random_value)

Секція 3. Розділ 1