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Lære Multinomial Distribution | Commonly Used Discrete Distributions
Probability Theory Basics

bookMultinomial Distribution

The multinomial scheme extends the Bernoulli trial in cases with more than two outcomes. A multinomial scheme refers to a situation where you have multiple categories or outcomes and are interested in studying the probabilities of each outcome occurring. A probability distribution that models the number of successes in a fixed number of independent trials with multiple categories is called multinomial distribution.

Example

A company is surveying to gather feedback from its customers.
The survey has three possible responses: "Satisfied," "Neutral," and "Dissatisfied." The company randomly selects 50 customers and records their responses.
Assume that each customer is satisfied with a probability 0.3, neutral with a probability 0.4, and dissatisfied with a probability 0.3.
Calculate the probability that there will be 25 "Satisfied" responses, 15 "Neutral," and 10 "Dissatisfied".

To solve this task multinomial distribution is used:

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import numpy as np from scipy.stats import multinomial # Define the probabilities of each response category probabilities = [0.3, 0.4, 0.3] # Satisfied, Neutral, Dissatisfied # Specify the number of responses for which we calculate probability response = [25, 15, 10] # 25 satisfied, 15 neutral, 10 dissatisfied responses out of 50 total responses # Calculate the probability mass function (pmf) using multinomial distribution pmf = multinomial.pmf(response, n=50, p=probabilities) print(f'Probability of {response}: {pmf:.4f}')
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In the code above, we used .pmf() method of scipy.stats.multinomial class with parameters n (number of trials) and p (probabilities of each outcome) to calculate probability that we will have certain response (the first argument of the .pmf() method.

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Seksjon 3. Kapittel 3

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bookMultinomial Distribution

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The multinomial scheme extends the Bernoulli trial in cases with more than two outcomes. A multinomial scheme refers to a situation where you have multiple categories or outcomes and are interested in studying the probabilities of each outcome occurring. A probability distribution that models the number of successes in a fixed number of independent trials with multiple categories is called multinomial distribution.

Example

A company is surveying to gather feedback from its customers.
The survey has three possible responses: "Satisfied," "Neutral," and "Dissatisfied." The company randomly selects 50 customers and records their responses.
Assume that each customer is satisfied with a probability 0.3, neutral with a probability 0.4, and dissatisfied with a probability 0.3.
Calculate the probability that there will be 25 "Satisfied" responses, 15 "Neutral," and 10 "Dissatisfied".

To solve this task multinomial distribution is used:

123456789101112
import numpy as np from scipy.stats import multinomial # Define the probabilities of each response category probabilities = [0.3, 0.4, 0.3] # Satisfied, Neutral, Dissatisfied # Specify the number of responses for which we calculate probability response = [25, 15, 10] # 25 satisfied, 15 neutral, 10 dissatisfied responses out of 50 total responses # Calculate the probability mass function (pmf) using multinomial distribution pmf = multinomial.pmf(response, n=50, p=probabilities) print(f'Probability of {response}: {pmf:.4f}')
copy

In the code above, we used .pmf() method of scipy.stats.multinomial class with parameters n (number of trials) and p (probabilities of each outcome) to calculate probability that we will have certain response (the first argument of the .pmf() method.

question mark

What is the multinomial distribution?

Select the correct answer

Alt var klart?

Hvordan kan vi forbedre det?

Takk for tilbakemeldingene dine!

Seksjon 3. Kapittel 3
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