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

Poisson Distribution 3/3

As you remember, with the .cdf() function, we can calculate the probability that the random variable will take a value less then or equal a defined number. Look at the example: Example 1/2:

The expected value of sunny days per month is 15. Calculate the probability that the number of sunny days will be less or equal 12.

Python realization:


              12345
            
import scipy.stats as stats

probability = stats.poisson.cdf(12, 15)

print("The probability is", probability * 100, "%")

Example 1/2:

The expected value of sunny days per month is 15. Calculate the probability that the number of sunny days will be less equal the number within the range from 5 to 11 (5; 11].

Python realization:


              1234567891011
            
import scipy.stats as stats


prob_1 = stats.poisson.cdf(11, 15)

prob_2 = stats.poisson.cdf(5, 15)


probability = prob_1 - prob_2

print("The probability is", probability * 100, "%")

When we subtract the second expression from the first, we leave the interval from 11 to 5 exclusive. Thus, using this calculation stats.poisson.cdf(11, 15), we will find the probability that our variable will take a value less than 11. And using this calculation stats.poisson.cdf(5, 15), we will find the probability that our variable will take a value less than or equal to 5.

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

Все було зрозуміло?

Секція 5. Розділ 3

Poisson Distribution 3/3

As you remember, with the .cdf() function, we can calculate the probability that the random variable will take a value less then or equal a defined number. Look at the example: Example 1/2:

The expected value of sunny days per month is 15. Calculate the probability that the number of sunny days will be less or equal 12.

Python realization:


              12345
            
import scipy.stats as stats

probability = stats.poisson.cdf(12, 15)

print("The probability is", probability * 100, "%")

Example 1/2:

The expected value of sunny days per month is 15. Calculate the probability that the number of sunny days will be less equal the number within the range from 5 to 11 (5; 11].

Python realization:


              1234567891011
            
import scipy.stats as stats


prob_1 = stats.poisson.cdf(11, 15)

prob_2 = stats.poisson.cdf(5, 15)


probability = prob_1 - prob_2

print("The probability is", probability * 100, "%")

Все було зрозуміло?

Секція 5. Розділ 3

Poisson Distribution 3/3

As you remember, with the .cdf() function, we can calculate the probability that the random variable will take a value less then or equal a defined number. Look at the example: Example 1/2:

The expected value of sunny days per month is 15. Calculate the probability that the number of sunny days will be less or equal 12.

Python realization:


              12345
            
import scipy.stats as stats

probability = stats.poisson.cdf(12, 15)

print("The probability is", probability * 100, "%")

Example 1/2:

The expected value of sunny days per month is 15. Calculate the probability that the number of sunny days will be less equal the number within the range from 5 to 11 (5; 11].

Python realization:


              1234567891011
            
import scipy.stats as stats


prob_1 = stats.poisson.cdf(11, 15)

prob_2 = stats.poisson.cdf(5, 15)


probability = prob_1 - prob_2

print("The probability is", probability * 100, "%")

Все було зрозуміло?

As you remember, with the .cdf() function, we can calculate the probability that the random variable will take a value less then or equal a defined number. Look at the example: Example 1/2:

The expected value of sunny days per month is 15. Calculate the probability that the number of sunny days will be less or equal 12.

Python realization:


              12345
            
import scipy.stats as stats

probability = stats.poisson.cdf(12, 15)

print("The probability is", probability * 100, "%")

Example 1/2:

The expected value of sunny days per month is 15. Calculate the probability that the number of sunny days will be less equal the number within the range from 5 to 11 (5; 11].

Python realization:


              1234567891011
            
import scipy.stats as stats


prob_1 = stats.poisson.cdf(11, 15)

prob_2 = stats.poisson.cdf(5, 15)


probability = prob_1 - prob_2

print("The probability is", probability * 100, "%")

Секція 5. Розділ 3