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 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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Vector Subspace in Linear Algebra Author: Bindeshwar Singh Kushwaha Institute: PostNetwork Academy Definition of a Subspace Let \( V \) be a vector space over a field \( K \) and let \( W \subseteq V \). Then \( W \) is a subspace of \( V \) if \( W \) is itself
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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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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 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 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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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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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 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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