Зміст курсу

Probability Theory Basics

1. Basic Concepts of Probability Theory

Stochastic Experiment and Random Event Probability and It's Properties Geometrical Probability Challenge: Solving the Task Using Geometric Probability Independence and Incompatibility of Random Events Conditional Probability

2. Probability of Complex Events

Inclusion-Exclusion Principle Challenge: Solving the Task Using Inclusion-Exclusion Principle The Multiplication Rule of Probability Law of Total Probability Bayes' Theorem Challenge: Solving the Task Using Bayes' Theorem

3. Commonly Used Discrete Distributions

Binomial Distribution Challenge: Solving Task Using Binomial Distribution Multinomial Distribution Geometric Distribution Poisson Distribution Challenge: Solving Task Using Poisson Distribution

4. Commonly Used Continuous Distributions

Continuous Uniform Distribution Exponential Distribution Challenge: Solving Task Using Exponential Distribution Gaussian Distribution Challenge: Solving Task Using Gaussian Distribution

5. Covariance and Correlation

What is Covariance?What is Correlation?Challenge: Solving the Task Using Correlation

Probability Theory Basics

Multinomial 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:

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.