Multinomial DistributionMultinomial 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.

Let's look at the 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:

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.


What is the multinomial distribution?

Select the correct answer

Everything was clear?

Section 3. Chapter 3