Bindeshwar S. Kushwaha

Introduction to Python Programming | Fundamentals and Examples

Programming, Python /

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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Introduction to Machine Learning

Artificial Intelligence, Data Handling, Machine Learning /

Introduction to Machine Learning Definition and Types Welcome to this detailed introduction to Machine Learning. This post explores the fundamental definitions, types of machine learning, and their mathematical representations. What is Machine Learning? What is Machine Learning? What are the different types of Machine Learning? How can we mathematically define each type? Definition of Machine

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Some Questions Based on Continuous Probability Distributions | Data Science & AI Lecture Series

Artificial Intelligence /

Some Questions Based on Continuous Probability Distributions Question Compute the conditional probability: \[ P\left(X > \frac{3}{4} \mid X > \frac{1}{2}\right) \] Theory Behind Solution The conditional probability formula: \[ P(A | B) = \frac{P(A \cap B)}{P(B)} \] For continuous random variables, probability is computed using integration. Understanding Probability Density Functions A probability density function (p.d.f.)

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A Beginner’s Guide to the Poisson Distribution with Real-World Examples

Uncategorized /

  A Beginner’s Guide to the Poisson Distribution with Real-World Examples Probability theory plays a crucial role in various real-world scenarios, particularly when dealing with random events that occur over a specific interval of time or space. One of the most widely used probability distributions for such scenarios is the Poisson distribution. This distribution helps

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Some Questions of Linear Algebra: Linear Transformation

Algebra /

  Some Questions of Linear Algebra: Linear Transformation Definition: Linear Transformation A linear transformation \(T: \mathbb{R}^n \to \mathbb{R}^m\) is a function that satisfies: Additivity: \(T(\mathbf{u} + \mathbf{v}) = T(\mathbf{u}) + T(\mathbf{v})\) for all \(\mathbf{u}, \mathbf{v} \in \mathbb{R}^n\). Homogeneity: \(T(c \mathbf{v}) = c T(\mathbf{v})\) for all \(\mathbf{v} \in \mathbb{R}^n\) and scalars \(c\). Numerical Example: Linear Transformation

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Central Limit Theorem (CLT) and Uniformly Minimum Variance Unbiased Estimator (UMVUE)

Artificial Intelligence, Data Handling, Research and Development, Statistics /

Central Limit Theorem (CLT) and Uniformly Minimum Variance Unbiased Estimator (UMVUE) By: Bindeshwar Singh Kushwaha Institute: PostNetwork Academy Question 1 Suppose \( X_1, X_2, \dots \) is an i.i.d. sequence of random variables with common variance \( \sigma^2 > 0 \). Define: \[ Y_n = \frac{1}{n} \sum_{i=1}^{n} X_{2i-1}, \quad Z_n = \frac{1}{n} \sum_{i=1}^{n} X_{2i} \]

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Continuous Random Variable and Probability Density Function

Artificial Intelligence, Machine Learning, Probability and Statistics, Research and Development, Statistics /

  Continuous Random Variable and Probability Density Function Data Science and A.I. Lecture Series Continuous Random Variable and Probability Density Function A random variable is continuous if it can take any real value within a given range. Instead of probability mass function, we use probability density function (PDF), denoted by \( f(x) \). The probability

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Some Questions Based on Discrete Probability Distributions

Artificial Intelligence, Machine Learning, Mathematics, Maths, Statistics /

Some Questions Based on Discrete Probability Distributions Data Science and A.I. Lecture Series   Problem 1 2 bad articles are mixed with 5 good ones. Find the probability distribution of the number of bad articles if 2 articles are drawn at random. Let \( X \) be the number of bad articles drawn. Possible values:

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Discrete Random Variable and Probability Mass Function

Artificial Intelligence, Mathematics, Maths, Probability and Statistics, Research and Development, Statistics /

  Discrete Random Variable and Probability Mass Function Data Science and A.I. Lecture Series A random variable is said to be discrete if it has either a finite or a countable number of values. Countable values are those which can be arranged in a sequence, corresponding to natural numbers. Example: Number of students present each

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Random Variables and Probability Distributions

Artificial Intelligence, Data Handling, Mathematics, Maths, Probability and Statistics, Research and Development, Statistics /

Random Variables and Probability Distributions Introduction to Random Variables In many experiments, we are interested in a numerical characteristic associated with outcomes of a random experiment. A random variable (RV) is a function that assigns a numerical value to each outcome of a random experiment. Example: Consider tossing a fair die twice and defining \(

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