Artificial Intelligence

Binomial Distribution Data Science and A.I. Lecture Series

  Binomial Distribution Data Science and A.I. Lecture Series By Bindeshwar Singh Kushwaha | PostNetwork Academy Binomial Probability Function The binomial probability function is given by: \[ P(X = k) = \binom{n}{k} p^k (1 – p)^{n – k} \] where: \( n \) = total number of trials \( k \) = number of successes […]

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Bernoulli Distribution in Probability and Statistics

Bernoulli Distribution Data Science and A.I. Lecture Series By Bindeshwar Singh Kushwaha | PostNetwork Academy Introduction to Bernoulli Distribution A Bernoulli trial is an experiment with only two possible outcomes: Success (1) and Failure (0). If p is the probability of success, then q = 1 – p is the probability of failure. A random

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Addition, Multiplication Theorem of Expectation and Covariance

Addition, Multiplication Theorem of Expectation and Covariance Data Science and A.I. Lecture Series By Bindeshwar Singh Kushwaha PostNetwork Academy Outline Introduction Addition Theorem of Expectation Proof of Addition Theorem Multiplication Theorem of Expectation Proof of Multiplication Theorem Covariance Introduction Expectation (or expected value) is a fundamental concept in probability and statistics. It provides a measure

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Moments and Other Measures in Terms of Expectations

  Moments and Other Measures in Terms of Expectations Data Science and A.I. Lecture Series By Bindeshwar Singh Kushwaha – PostNetwork Academy Moments The \( r^{th} \) order moment about any point \( A \) of a variable \( X \) is given by: For discrete variables: \[ \mu_r’ = \sum_{i=1}^{n} p_i (x_i – A)^r

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Mathematical Expectation

Mathematical Expectation Data Science and A.I. Lecture Series By Bindeshwar Singh Kushwaha – PostNetwork Academy Introduction This unit explores the expectation of a random variable. Expectation provides a measure of central tendency in probability distributions. Expectation is useful in both discrete and continuous probability distributions. Problems and examples help in understanding practical applications. Objectives Define

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Operators in Python Programming

  Operators in Python Data Science and A.I. Lecture Series Author: Bindeshwar Singh Kushwaha | Institute: PostNetwork Academy Introduction Operators in Python are special symbols that perform computations on operands. Python provides various types of operators: Arithmetic Operators Relational Operators Logical Operators Bitwise Operators Assignment Operators Membership Operators Identity Operators Arithmetic Operators a = 10

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IBM Research and Hugging Face Introduce SmolDocling: A Compact Vision-Language Model for Document Conversion

IBM Research and Hugging Face Introduce SmolDocling: A Compact Vision-Language Model for Document Conversion IBM Research and Hugging Face have unveiled SmolDocling, an ultra-compact vision-language model designed for end-to-end document conversion. Unlike traditional models that rely on large foundational architectures or complex pipelines, SmolDocling offers a lightweight, efficient solution for processing entire documents while preserving

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Bivariate Discrete Cumulative Distribution Function

Bivariate Discrete Cumulative Distribution Function Data Science and A.I. Lecture Series Author: Bindeshwar Singh Kushwaha Institute: PostNetwork Academy Joint and Marginal Distribution Functions for Discrete Random Variables Two-Dimensional Joint Distribution Function The distribution function of the two-dimensional random variable \((X, Y)\) for all real \(x\) and \(y\) is defined as: \[ F(x,y) = P(X \leq

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Continuous Cumulative Distribution Function (CDF) | Probability & Statistics

  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: Step-by-Step Guide with Derivation & Visualization

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

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