Bivariate Discrete Random Variables Data Science and A.I. Lecture Series By Bindeshwar Singh Kushwaha, PostNetwork Academy Definition Let \( X \) and \( Y \) be two discrete random variables defined on the sample space \( S \) of a random experiment. Then, the function \( (X, Y) \) defined on the same sample space […]
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Definition: Continuous CDF A continuous random variable can take an infinite number of values in a given range. The Probability Density Function (PDF) \( f(x) \) describes the likelihood of \( X \) falling within a small interval. The Cumulative Distribution Function (CDF) is given by: \[ F(x) = P[X \leq x] = \int_{-\infty}^{x}
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Ordinary Least Squares (OLS) Regression Author: Bindeshwar Singh Kushwaha Institute: PostNetwork Academy Dataset of a Company X (Budget) Y (Sales) 1 2 2 2.8 3 3.6 4 4.5 5 5.1 Description: The dataset represents the relationship between advertising budget (\(X\)) and sales revenue (\(Y\)). The company wants to analyze how the budget affects sales using
Definition of Differential Equations A differential equation is an equation that involves one or more derivatives of an unknown function. Example: \[ \frac{dy}{dx} = 3x^2 \] Types of Differential Equations Ordinary Differential Equations (ODEs): \( \frac{dy}{dx} + 2y = x^2 \) Partial Differential Equations (PDEs): \( \frac{\partial u}{\partial x} + \frac{\partial u}{\partial y} = 0
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Tokens in Python Introduction Tokens are the smallest individual units in a Python program. Everything in a Python program is built using tokens. Python has five types of tokens: Keywords: Reserved words in Python. Identifiers: Names given to variables, functions, and classes. Literals: Fixed values such as numbers, strings, and boolean values. Operators: Symbols
What is an Expression in Python? An expression in Python is a combination of values, variables, and operators that produces a value when evaluated. Example: x = 10 + 5 Operator Precedence in Python Python follows the PEMDAS rule to evaluate expressions: P: Parentheses E: Exponentiation MD: Multiplication and Division (left to right) AS:
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Vectors in \(\mathbb{R}^n\) and \(\mathbb{C}^n\) Introduction to Vectors A vector is a mathematical object that has both magnitude and direction. Vectors are essential in physics, engineering, and mathematics. They can be represented in different dimensions, such as real number space \(\mathbb{R}^n\) and complex number space \(\mathbb{C}^n\). Visualization of Vectors in \(\mathbb{R}^3\) Consider a three-dimensional space
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The Rise of Generative AI: Overview Unlike traditional AI systems that rely on predefined rules, generative AI models use vast datasets and deep learning techniques to generate novel and contextually relevant outputs. This transformative capability is reshaping industries such as content creation, education, healthcare, and entertainment. How Generative AI Works At its core, generative
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Supervised Learning in Machine Learning Introduction Supervised learning is a machine learning technique where a model learns from labeled data. The dataset consists of input features \((x_1, x_2, x_3)\) and an output label \(y\). The goal is to find a function that maps inputs to correct outputs. Features and Labels in a Dataset A
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Introduction to Python Programming Fundamentals and Examples Welcome to this introduction to Python programming. This post covers the fundamentals of Python, including its definition, programming concepts, and example codes. What is a Program? A program is a sequence of instructions that a computer can execute. Programs help automate tasks and solve problems. They consist of
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