Maths and Probability

Vectors

What is a Vector?

• A vector is a list of numbers representing features

Vector Representation

• Example: [x1, x2, x3]

Vector Operations

• Vector addition

• Vector multiplication

Vector Equations

• Mathematical form of feature representation

Usage of Vectors in Machine Learning

• Represent input features

• Used in distance calculations

• Used in model equations

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Matrices

What is a Matrix?

• A collection of vectors arranged in rows and columns

Matrix Representation

• Represents datasets

Matrix Operations

• Matrix addition

• Matrix multiplication

Matrix Equations

• Used for large-scale computations

Usage of Matrices in Machine Learning

• Store datasets

• Perform bulk operations

• Model training computations

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Probability Basics

What is Probability?

• Measure of likelihood of an event

• Range: 0 to 1

Independent Events

• One event does not affect another

• Example: coin toss and dice roll

Dependent Events

• One event affects another

• Example: drawing cards without replacement

Probability Formulas

• P(A) = favorable / total

• P(Not A) = 1 − P(A)

• Independent: P(A ∩ B) = P(A) × P(B)

• Dependent: P(A ∩ B) = P(A) × P(B | A)

Importance of Probability in Machine Learning

• Handles uncertainty

• Produces confidence-based predictions

Usage of Probability in ML Models

• Naive Bayes

• Logistic Regression

• Spam detection

• Recommendation systems