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 2/3

As you remember, with the .pmf() function, we can calculate the probability over a range using the addition rule. Look at the example: Example 1/2: We know that per day the expected value of users is 100. Calculate the probability that 110 users will visit the app. This distribution is discrete, so to calculate the probability of getting the exact number of customers, we can use the .pmf() function with two parameters: the first is our desored number of events, and the second is lambda.

Python realization:

We will use .pmf() function for the Poisson distribution using stats.poisson.pmf().


              123
            
import scipy.stats as stats
probability = stats.poisson.pmf(110, 100)
print("The probability is", probability * 100, "%")

Example 2/2:

The expected value of sunny days per month is 15. Calculate the probability that the number of sunny days will equal 16, 17, 18, or 19.

Python realization:


              12345678910
            
import scipy.stats as stats

prob_1 = stats.poisson.pmf(16, 15)
prob_2 = stats.poisson.pmf(17, 15)
prob_3 = stats.poisson.pmf(18, 15)
prob_4 = stats.poisson.pmf(19, 15)

probability = prob_1 + prob_2 + prob_3 + prob_4

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

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 2

Poisson Distribution 2/3

Python realization:

We will use .pmf() function for the Poisson distribution using stats.poisson.pmf().


              123
            
import scipy.stats as stats
probability = stats.poisson.pmf(110, 100)
print("The probability is", probability * 100, "%")

Example 2/2:

The expected value of sunny days per month is 15. Calculate the probability that the number of sunny days will equal 16, 17, 18, or 19.

Python realization:


              12345678910
            
import scipy.stats as stats

prob_1 = stats.poisson.pmf(16, 15)
prob_2 = stats.poisson.pmf(17, 15)
prob_3 = stats.poisson.pmf(18, 15)
prob_4 = stats.poisson.pmf(19, 15)

probability = prob_1 + prob_2 + prob_3 + prob_4

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

Все було зрозуміло?

Секція 5. Розділ 2

Poisson Distribution 2/3

Python realization:

We will use .pmf() function for the Poisson distribution using stats.poisson.pmf().


              123
            
import scipy.stats as stats
probability = stats.poisson.pmf(110, 100)
print("The probability is", probability * 100, "%")

Example 2/2:

The expected value of sunny days per month is 15. Calculate the probability that the number of sunny days will equal 16, 17, 18, or 19.

Python realization:


              12345678910
            
import scipy.stats as stats

prob_1 = stats.poisson.pmf(16, 15)
prob_2 = stats.poisson.pmf(17, 15)
prob_3 = stats.poisson.pmf(18, 15)
prob_4 = stats.poisson.pmf(19, 15)

probability = prob_1 + prob_2 + prob_3 + prob_4

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

Все було зрозуміло?

Python realization:

We will use .pmf() function for the Poisson distribution using stats.poisson.pmf().


              123
            
import scipy.stats as stats
probability = stats.poisson.pmf(110, 100)
print("The probability is", probability * 100, "%")

Example 2/2:

The expected value of sunny days per month is 15. Calculate the probability that the number of sunny days will equal 16, 17, 18, or 19.

Python realization:


              12345678910
            
import scipy.stats as stats

prob_1 = stats.poisson.pmf(16, 15)
prob_2 = stats.poisson.pmf(17, 15)
prob_3 = stats.poisson.pmf(18, 15)
prob_4 = stats.poisson.pmf(19, 15)

probability = prob_1 + prob_2 + prob_3 + prob_4

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

Секція 5. Розділ 2