Course Content

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 1/3

What is it?

This distribution describes the probability that events occur in a fixed interval of time or space if they happen with a known constant mean rate and independently.

Examples:

Website visitors per month.
The number of meteors that will fall per hour.
The number of people die because of specific diseases.

Lambda in Poisson distribution:

Lambda is the key parameter of the distribution that represents its expected value. It can be defined as a mean number of events within a specified time or space.

Example with lambda:

Lambda represents the expected value; if our expected value of customers visiting the app per day is 10000, then the lambda, in this case, equals 10000.


              123456789
            
import scipy.stats as stats
import matplotlib.pyplot as plt
import seaborn as sns

# Simulating Poisson distribution
data = stats.poisson.rvs(1000, size = 1000)
sns.histplot(data = data)

plt.show()

.rvs() - function that is used to create a random distribution. The first argument is lambda and the second is the size of the sample. - .poisson - referring to the poisson object to work with Poisson distribution.

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

Everything was clear?

Section 5. Chapter 1

Poisson Distribution 1/3

What is it?

This distribution describes the probability that events occur in a fixed interval of time or space if they happen with a known constant mean rate and independently.

Examples:

Website visitors per month.
The number of meteors that will fall per hour.
The number of people die because of specific diseases.

Lambda in Poisson distribution:

Lambda is the key parameter of the distribution that represents its expected value. It can be defined as a mean number of events within a specified time or space.

Example with lambda:

Lambda represents the expected value; if our expected value of customers visiting the app per day is 10000, then the lambda, in this case, equals 10000.


              123456789
            
import scipy.stats as stats
import matplotlib.pyplot as plt
import seaborn as sns

# Simulating Poisson distribution
data = stats.poisson.rvs(1000, size = 1000)
sns.histplot(data = data)

plt.show()

.rvs() - function that is used to create a random distribution. The first argument is lambda and the second is the size of the sample. - .poisson - referring to the poisson object to work with Poisson distribution.

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

Everything was clear?

Section 5. Chapter 1

Poisson Distribution 1/3

What is it?

This distribution describes the probability that events occur in a fixed interval of time or space if they happen with a known constant mean rate and independently.

Examples:

Website visitors per month.
The number of meteors that will fall per hour.
The number of people die because of specific diseases.

Lambda in Poisson distribution:

Lambda is the key parameter of the distribution that represents its expected value. It can be defined as a mean number of events within a specified time or space.

Example with lambda:

Lambda represents the expected value; if our expected value of customers visiting the app per day is 10000, then the lambda, in this case, equals 10000.


              123456789
            
import scipy.stats as stats
import matplotlib.pyplot as plt
import seaborn as sns

# Simulating Poisson distribution
data = stats.poisson.rvs(1000, size = 1000)
sns.histplot(data = data)

plt.show()

.rvs() - function that is used to create a random distribution. The first argument is lambda and the second is the size of the sample. - .poisson - referring to the poisson object to work with Poisson distribution.

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

Everything was clear?

What is it?

This distribution describes the probability that events occur in a fixed interval of time or space if they happen with a known constant mean rate and independently.

Examples:

Website visitors per month.
The number of meteors that will fall per hour.
The number of people die because of specific diseases.

Lambda in Poisson distribution:

Lambda is the key parameter of the distribution that represents its expected value. It can be defined as a mean number of events within a specified time or space.

Example with lambda:

Lambda represents the expected value; if our expected value of customers visiting the app per day is 10000, then the lambda, in this case, equals 10000.


              123456789
            
import scipy.stats as stats
import matplotlib.pyplot as plt
import seaborn as sns

# Simulating Poisson distribution
data = stats.poisson.rvs(1000, size = 1000)
sns.histplot(data = data)

plt.show()

.rvs() - function that is used to create a random distribution. The first argument is lambda and the second is the size of the sample. - .poisson - referring to the poisson object to work with Poisson distribution.

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

Section 5. Chapter 1

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