Course Content

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

Geometric Distribution

The geometric distribution is a probability distribution that models the number of experiments on which we first get a successful outcome in a sequence of independent Bernoulli trials.

Note
Admit that geometrical distribution and geometric probability are two different concepts.
The first one is the distribution that describes the order number of the first successful experiment in the Bernoulli process. The second one is the extension of the classical rule for determining probabilities to the case of an uncountable number of possible outcomes of an experiment.

Each trial has two possible outcomes in the geometric distribution: success (with probability p) or failure (with probability q = 1 - p). The distribution is characterized by a single parameter, p, representing the probability of success in each trial.

Suppose you hit the target with a probability of 0.4. Calculate the probability that your fourth shot will be the first successful.


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from scipy.stats import geom

# Probability of success (correct answer)
proba = 0.4

# Calculate probability that 4'th shot will be the first successful
pmf = geom.pmf(4, p=proba)
# Print the results
print(f'Corresponding probability equals {pmf:.4f}')

In the code above, we used .pmf() method with parameter p (probability of success) to calculate the corresponding probability in point 4.

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Section 3. Chapter 4