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Probability Theory Update
course content

Course Content

Probability Theory Update

Probability Theory Update

1. Probability Basics
Set TheoryProbability ExperimentStatistical Independence
2. Statistical Dependence
Dependent EventsMutually Exclusive EventsAddition Rule for Mutually Exclusive EventsAddition Rule for Non-Mutually Exclusive EventsMultiplication Rule for Independent EventsMultiplication Rule for Dependent EventsConditional probabilityBayes Rule
3. Learn Crucial Terms
Random VariableDiscrete vs Continuous Random VariableExpected ValueThe Law of Large NumbersCMT
4. Probability Functions
Binomial DistributionProbability Mass Function (PMF) 1/2Probability Mass Function (PMF) 2/2Cumulative Distribution Function (CDF) 1/2Cumulative Distribution Function (CDF) 2/2Probability Density Function (PDF) 1/2Probability Density Function (PDF) 2/2
5. Distributions
Poisson Distribution 1/3Poisson Distribution 2/3Poisson Distribution 3/3Standard Normal Distribution (Gaussian distribution) 1/2

bookPoisson 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, "%")
copy

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, "%")
copy

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Section 5. Chapter 2
toggle bottom row

bookPoisson 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, "%")
copy

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, "%")
copy

Switch to desktopSwitch to desktop for real-world practiceContinue from where you are using one of the options below
Everything was clear?

How can we improve it?

Thanks for your feedback!

Section 5. Chapter 2
toggle bottom row

bookPoisson 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, "%")
copy

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, "%")
copy

Switch to desktopSwitch to desktop for real-world practiceContinue from where you are using one of the options below
Everything was clear?

How can we improve it?

Thanks for your feedback!

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, "%")
copy

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, "%")
copy

Switch to desktopSwitch to desktop for real-world practiceContinue from where you are using one of the options below
Section 5. Chapter 2
Switch to desktopSwitch to desktop for real-world practiceContinue from where you are using one of the options below
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