PostNetwork Academy

Moments of Binomial Distribution Video I Data Science and A.I. Lect. Series

Artificial Intelligence, Machine Learning, Probability and Statistics, Research and Development, Statistics / Bindeshwar S. Kushwaha

Moments of Binomial Distribution By Bindeshwar Singh Kushwaha — PostNetwork Academy Moment Definition Let \( X \sim B(n, p) \) be a binomial random variable. The \( r^\text{th} \) raw moment about origin: \( \mu_r’ = \mathbb{E}(X^r) = \sum_{x=0}^{n} x^r \cdot \mathbb{P}(X = x) \) First-order moment (mean): \( \mu_1′ = \mathbb{E}(X) \) Binomial

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Ordinary Differential Equation Questions and Solutions

Uncategorized / Bindeshwar S. Kushwaha

Solving First Order and First Degree Differential Equations Author: Bindeshwar Singh Kushwaha Institute: PostNetwork Academy Example 1: Solve \( \frac{dy}{dx} = e^x \) Equation: \( \frac{dy}{dx} = e^x \) Multiply both sides by \( dx \): \( dy = e^x dx \) Integrate: \( \int dy = \int e^x dx \) Solution: \( y =

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Linear Combinations and Spanning Sets

Artificial Intelligence, Linear Algebra / Bindeshwar S. Kushwaha

Linear Combinations and Spanning Sets Author: Bindeshwar Singh Kushwaha Institute: PostNetwork Academy Introduction: In this post, we will explore the concepts of Linear Combinations and Spanning Sets in the context of vector spaces in Linear Algebra. Linear Combinations and Spanning Sets Let V be a vector space over a field K. A vector v in

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Vector and Vector Space in Linear Algebra

Algebra, Artificial Intelligence, Linear Algebra / Bindeshwar S. Kushwaha

Vector and Vector Space in Linear Algebra by Bindeshwar Singh Kushwaha PostNetwork Academy Definition of ℝn The set of all n-tuples of real numbers is denoted by ℝn: u = (a1, a2, …, an) Each u is called a point or vector. The components ai are called coordinates, components, entries, or elements. The term scalar

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Examples Based on Binomial Probability Distribution

Machine Learning, Probability and Statistics, Research and Development, Statistics / Bindeshwar S. Kushwaha

Binomial Distribution Overview A discrete random variable \( X \) is said to follow a binomial distribution with parameters \( n \) and \( p \) if it takes on values \( x = 0, 1, 2, …, n \) with the probability mass function: \[ P(X = x) = \binom{n}{x} p^x q^{n – x},

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But What A Neural Network Learns Actually: Neural Network Architecture for Iris Data Set

Artificial Intelligence, Machine Learning, PyTorch, Research and Development / Bindeshwar S. Kushwaha

Neural Network Architecture for Iris Dataset Author: Bindeshwar Singh Kushwaha Institution: PosstNetwork Academy Outline Iris Dataset Overview Neural Network Architecture Mathematical Formulation Code Walkthrough Live Loss Plot Evaluation and Summary Sample from Iris Dataset Sepal Length Sepal Width Petal Length Petal Width Class 5.1 3.5 1.4 0.2 Setosa 6.2 2.9 4.3 1.3 Versicolor 5.9 3.0

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Object-Oriented Programming in Python

Programming, Python / Bindeshwar S. Kushwaha

Object-Oriented Programming in Python By: Bindeshwar Singh Kushwaha Institute: PostNetwork Academy What is Object-Oriented Programming (OOP)? OOP is a programming paradigm. It is based on the concept of “objects”. Helps model real-world entities like BankAccount, Student, Car. Makes code more organized, reusable, and easier to maintain. Class in OOP A class is a blueprint

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Transpose of a Matrix in PyTorch

Algebra, Artificial Intelligence, Linear Algebra, Machine Learning, PyTorch, Research and Development / Bindeshwar S. Kushwaha

Transpose of a Matrix Author: Bindeshwar Singh Kushwaha Institute: PostNetwork Academy What is the Transpose of a Matrix? The transpose of a matrix \( A \), denoted \( A^T \), is obtained by interchanging rows and columns. If \( A = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix} \),

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Matrix Operations with PyTorch | Learn Linear Algebra with Code

Artificial Intelligence, Generative A. I., Linear Algebra, Machine Learning, Mathematics, Python, PyTorch / Bindeshwar S. Kushwaha

Matrix Operations with PyTorch Author: Bindeshwar Singh Kushwaha Institute: PostNetwork Academy Matrix Addition and Scalar Multiplication Matrix Addition: We add corresponding elements of the same-sized matrices: \( A + B = [a_{ij} + b_{ij}] \) Scalar Multiplication: Multiply each element of the matrix by the scalar value: \( kA = [k \cdot a_{ij}] \) Example:

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Understanding PyTorch: Tensors, Vectors, and Matrices

PyTorch / Bindeshwar S. Kushwaha

Understanding PyTorch: Tensors, Vectors, and Matrices By: Bindeshwar Singh Kushwaha Institute: PostNetwork Academy What is PyTorch? PyTorch is an open-source deep learning framework. It supports dynamic computation graphs. Designed to be Pythonic and flexible. Commonly used for research and production in AI/ML. Types of Tensors A scalar is a 0-dimensional tensor. A vector is a

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