Fitting Binomial Distribution | Data Science and A.I. Lecture Series

Artificial Intelligence, Data Handling, Probability and Statistics, Statistics /

Fitting Binomial Distribution Introduction Fitting a binomial distribution involves comparing observed frequencies with expected frequencies derived from the binomial probability formula. The recurrence relation simplifies the process of finding probabilities. This technique is useful for testing if a dataset follows a binomial distribution. Binomial Probability Function The binomial probability function is: $$p(x) = {n \choose

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Introduction to Robotics Simulation with PyBullet

Robotics /

Introduction to Robotics Simulation with PyBullet Author: Bindeshwar Singh Kushwaha Institute: PostNetwork Academy What is Robotics? Robotics is an exciting and fast-growing interdisciplinary field that combines mechanical engineering, electrical engineering, computer science, and control systems. Robots are programmable machines capable of performing tasks automatically or semi-automatically, either with minimal human intervention or fully autonomously. The

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Span and Intersection of Subspaces | Linear Algebra Explained

Linear Algebra /

Span and Intersection of Subspaces Author: Bindeshwar Singh Kushwaha Institute: PostNetwork Academy Linear Span: Definition and Properties Given vectors \( u_1, u_2, \ldots, u_m \) in a vector space \( V \), their linear span is the set of all linear combinations: \[ \text{span}(u_1, u_2, \ldots, u_m) = \{ a_1 u_1 + a_2 u_2 +

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The Regression Revolution: How Sir Francis Galton’s Work Laid the Groundwork for Neural Networks

Research and Development /

  Author: Bindeshwar Singh Kushwaha Institute: PostNetwork Academy Sir Francis Galton: Biography and Contributions Quick Facts Name: Sir Francis Galton, FRS FRAI Born: 16 February 1822, Birmingham, England Died: 17 January 1911, Haslemere, Surrey, England (Aged 88) Resting Place: Claverdon, Warwickshire, England Education: King’s College London, Trinity College Cambridge Father: Samuel Tertius Galton Relatives: Charles

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Research

What is Research? How to Write a Research Paper

Research and Development /

What is Research? How to Write a Research Paper Author: Bindeshwar Singh Kushwaha Institute: PostNetwork Academy Outline What is Research? Benefits of Research Research Paper Sections Research Paper Examples Where to Publish Research Papers What is Peer Review? What is Impact Factor? Where to Start from? What is Research? Systematic investigation to discover new knowledge

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Moment Generating Function of Binomial Distribution

Artificial Intelligence, Generative A. I., Machine Learning, Probability and Statistics, Statistics /

Moment Generating Function of Binomial Distribution Author: Bindeshwar Singh Kushwaha Institute: PostNetwork Academy Definition of Moment Generating Function The moment generating function (m.g.f.) of a random variable \( X \) is defined as: \[ M_X(t) = E(e^{tX}) \] For a continuous random variable: \[ M_X(t) = \int_{-\infty}^{\infty} e^{tx} f(x) \, dx \] For a discrete

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Solving First Order and First Degree Differential Equations

Calculus, Differential Equation /

Solving First Order and First Degree Differential Equations Author: Bindeshwar Singh Kushwaha Institute: PostNetwork Academy Reducing to Homogeneous Form Consider the differential equation of the form: $$\frac{dy}{dx} = \frac{a x + b y + c}{a’ x + b’ y + c’}$$ To reduce it to homogeneous form, use the substitution: $$x = X + h,

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

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

  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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