Канал: Iqbal Shahid

Erlang 2 Distribution Derivation of pdf by Basic Principles

Erlang 2 Distribution Derivation of pdf by Basic Principles

Problem solving using Mathematical Induction

Problem solving using Mathematical Induction

Unit vectors in Rectangular, Cylindrical and Spherical Coordinates

Unit vectors in Rectangular, Cylindrical and Spherical Coordinates

Planes: Equation, Distance from a Point and Examples

Planes: Equation, Distance from a Point and Examples

Triple Vector Product Identities and Jacobi Identity

Triple Vector Product Identities and Jacobi Identity

Vector Product, Triple Product and Example

Vector Product, Triple Product and Example

Vector analysis: One solved problem on Triangle's medians

Vector analysis: One solved problem on Triangle's medians

Boole's Inequality: Statement and Proof

Boole's Inequality: Statement and Proof

Rayleigh Distribution: Derivation of pdf

Rayleigh Distribution: Derivation of pdf

Limiting Ratio and GCD of adjacent Fibbonacci Numbers

Limiting Ratio and GCD of adjacent Fibbonacci Numbers

Maximizing Volume to Surface Area Ratio for a Rectangular Prism

Maximizing Volume to Surface Area Ratio for a Rectangular Prism

Probability Mixtures and Parametric Mixtures

Probability Mixtures and Parametric Mixtures

Application of Generating Functions - Python Script for Polynomial Multiplication

Application of Generating Functions - Python Script for Polynomial Multiplication

Application of Binomial Theorem: Simplifying a Sum

Application of Binomial Theorem: Simplifying a Sum

Order Statistics: Derivation of pdf and Example

Order Statistics: Derivation of pdf and Example

Cylindrical and Spherical Coordinates: Solved Examples

Cylindrical and Spherical Coordinates: Solved Examples

Surface of Revolution - Equation and Examples

Surface of Revolution - Equation and Examples

Cylinder - Directrix and Ruling: Examples

Cylinder - Directrix and Ruling: Examples

Radical Planes: Solved Problems

Radical Planes: Solved Problems

Planes: Distance from a point and Distance between Skew Lines

Planes: Distance from a point and Distance between Skew Lines

Planes: Equation from 3 Points and Sketching

Planes: Equation from 3 Points and Sketching

Parametric Forms for Lines in Space: Solved Examples

Parametric Forms for Lines in Space: Solved Examples

Vector Product: Some Solved Examples

Vector Product: Some Solved Examples

Function of Two Random Variables: Difference(Z = X - Y)

Function of Two Random Variables: Difference(Z = X - Y)

Function of two random variables: Quotient (Z = X/Y), pdf derivation and examples

Function of two random variables: Quotient (Z = X/Y), pdf derivation and examples

Markov and Chebyshev Inequalities - Proofs and Example

Markov and Chebyshev Inequalities - Proofs and Example

Random Variable Transformation: Continuous Case - Example

Random Variable Transformation: Continuous Case - Example

Quadratic Residues: Definition, Example and Calculating how many can be found

Quadratic Residues: Definition, Example and Calculating how many can be found

Random Variable Transformation: Discrete Case

Random Variable Transformation: Discrete Case

Weibull Distribution: Mean and Variance

Weibull Distribution: Mean and Variance

Beta Distribution: Mean and Variance

Beta Distribution: Mean and Variance

Designing a Turing Machine to accept a Regular Set

Designing a Turing Machine to accept a Regular Set

Probability Integral Transform and Standard Uniform Distribution (Analytical and Matlab-based proof)

Probability Integral Transform and Standard Uniform Distribution (Analytical and Matlab-based proof)

Laplace Distribution: Mean and Variance

Laplace Distribution: Mean and Variance

Memoryless Property and the Exponential Distribution

Memoryless Property and the Exponential Distribution

Log-Normal Distribution: Mean and Variance

Log-Normal Distribution: Mean and Variance

Discrete Uniform Distribution: Introduction, Mean and Variance

Discrete Uniform Distribution: Introduction, Mean and Variance

Binomial Distribution: Recursive Representation

Binomial Distribution: Recursive Representation

Turing Machine - Introduction and Example

Turing Machine - Introduction and Example

Distuingishable Strings and The Set of Palindromes

Distuingishable Strings and The Set of Palindromes

Pumping Lemma: Statement, Proof and Application

Pumping Lemma: Statement, Proof and Application

Regular Sets and Regular Grammars

Regular Sets and Regular Grammars

Regular Expression for a Finite State Automaton: Kleene's Theorem Part II

Regular Expression for a Finite State Automaton: Kleene's Theorem Part II

Finite State Automaton for a Regular Expression: Kleene's Theorem Part 1

Finite State Automaton for a Regular Expression: Kleene's Theorem Part 1

Regular Sets and their String Representations

Regular Sets and their String Representations

Non Deterministic Finite State Automaton: Representation and DFA Equivalence

Non Deterministic Finite State Automaton: Representation and DFA Equivalence

Multinomial Distribution: Covariance

Multinomial Distribution: Covariance

Multinomial Distribution: Variance

Multinomial Distribution: Variance

Multinomial Distribution: Expected Value

Multinomial Distribution: Expected Value

Multinomial Distribution: Introduction and Example

Multinomial Distribution: Introduction and Example

Finite State Automaton and Language Recognition (Part II): Examples

Finite State Automaton and Language Recognition (Part II): Examples

Finite State Automata and Language Recognition: Introduction and Examples

Finite State Automata and Language Recognition: Introduction and Examples

String Concatenation, Kleene's Closure and Examples

String Concatenation, Kleene's Closure and Examples

Finite State Machines: Mealy and Moore Types with Example

Finite State Machines: Mealy and Moore Types with Example

Finite State Machines - State Table, State Diagram and Sequence of Inputs

Finite State Machines - State Table, State Diagram and Sequence of Inputs

Phrase Structure Grammars - Derivation Trees and Backus-Naur Form

Phrase Structure Grammars - Derivation Trees and Backus-Naur Form

Constructing a Context Free Grammar to Generate all Signed Decimal Numbers

Constructing a Context Free Grammar to Generate all Signed Decimal Numbers

Types of Phrase Structure Grammar

Types of Phrase Structure Grammar

Phrase Structure Grammar: Validating and Generating a Language

Phrase Structure Grammar: Validating and Generating a Language

Karnaugh Maps for Sum of Products and Product of Sums

Karnaugh Maps for Sum of Products and Product of Sums

Boolean Function Representation - Sum of Products and Product of Sums

Boolean Function Representation - Sum of Products and Product of Sums

Quine McCluskey Method: Examples with three and four variables

Quine McCluskey Method: Examples with three and four variables

Logic Circuits: Two Bit Comparator

Logic Circuits: Two Bit Comparator

Logic Circuits: Half Adder and Full Adder

Logic Circuits: Half Adder and Full Adder

Hypergeometric Distribution: Variance

Hypergeometric Distribution: Variance

Boolean Algebra - Functional Completeness

Boolean Algebra - Functional Completeness

Boolean Algebra - Expressions, Functions and Duality

Boolean Algebra - Expressions, Functions and Duality

Minimum Spanning Trees - Prim's Algorithm and Kruskal's Algorithm

Minimum Spanning Trees - Prim's Algorithm and Kruskal's Algorithm

Hypergeometric Distribution - Expected Value

Hypergeometric Distribution - Expected Value

Spanning Tree Formation by Breadth First Search Algorithm

Spanning Tree Formation by Breadth First Search Algorithm

Spanning Tree Formation by Depth First Search (or Backtracking)

Spanning Tree Formation by Depth First Search (or Backtracking)

Tree Traversal - Prefix (Polish) and Postfix (Reverse Polish) Notations

Tree Traversal - Prefix (Polish) and Postfix (Reverse Polish) Notations

Tree traversal: PreOrder, InOrder and PostOrder Examples

Tree traversal: PreOrder, InOrder and PostOrder Examples

Application of Trees: Prefix Codes, Huffman coding for binary and m-ary case

Application of Trees: Prefix Codes, Huffman coding for binary and m-ary case

Non-Isomorphic Trees of degree 5 and maximum number of leaves in a tree

Non-Isomorphic Trees of degree 5 and maximum number of leaves in a tree

Vectors in Three Dimensions: Example on Dot Product and Orthogonality

Vectors in Three Dimensions: Example on Dot Product and Orthogonality

A quadrilateral is a parallelogram if and only if its diagonals bisect each other

A quadrilateral is a parallelogram if and only if its diagonals bisect each other

Planar Graphs: Applications of Euler's Formula

Planar Graphs: Applications of Euler's Formula

Vectors in Two Dimensions: Regular Polygons

Vectors in Two Dimensions: Regular Polygons

Vectors in Two Dimensions: Sum of a Number of Vectors

Vectors in Two Dimensions: Sum of a Number of Vectors

Vectors in Two Dimensions: Linear Combination of Vectors

Vectors in Two Dimensions: Linear Combination of Vectors

Dijkstra's Algorithm: An Example

Dijkstra's Algorithm: An Example

Hamilton Paths, Hamilton Circuits and Complete Bipartite Graphs

Hamilton Paths, Hamilton Circuits and Complete Bipartite Graphs

Hamilton Circuits: Ore's Theorem (Statement and Proof)

Hamilton Circuits: Ore's Theorem (Statement and Proof)

Euler Paths and Circuits: Fleury's Algorithm

Euler Paths and Circuits: Fleury's Algorithm

Graphs: The farmer, wolf, goat and cabbage puzzle

Graphs: The farmer, wolf, goat and cabbage puzzle

Graphs: Articulation Points and Bridges

Graphs: Articulation Points and Bridges

Graphs: Paths and Connectivity

Graphs: Paths and Connectivity

Graph Isomorphism and Self Complementary Graphs

Graph Isomorphism and Self Complementary Graphs

Graphs: Adjacency and Incidence Matrices for Cycles and Wheels

Graphs: Adjacency and Incidence Matrices for Cycles and Wheels

Maximum edges for a Bipartite Graph, Maximum and minimum degree in a graph, and Union of Graphs

Maximum edges for a Bipartite Graph, Maximum and minimum degree in a graph, and Union of Graphs

Graphs: Definitions, Union of Graphs and Bipartite Graphs

Graphs: Definitions, Union of Graphs and Bipartite Graphs

Partial Orderings and Hasse Diagrams

Partial Orderings and Hasse Diagrams

Equivalence Relations, Equivalence Classes and Partitions

Equivalence Relations, Equivalence Classes and Partitions

Warshall's Algorithm - Transitive Closure

Warshall's Algorithm - Transitive Closure

Transitive Closure

Transitive Closure

Composition of Relations and Transitivity

Composition of Relations and Transitivity

Relations, Properties and Digraphs - Examples

Relations, Properties and Digraphs - Examples

Relations, Properties and Matrices - Examples

Relations, Properties and Matrices - Examples

Derangements: An Application of Recursion

Derangements: An Application of Recursion

Derangements - An Application of the Inclusion Exclusion Principle

Derangements - An Application of the Inclusion Exclusion Principle

Inclusion Exclusion Principle: Proof and Example

Inclusion Exclusion Principle: Proof and Example

Generating Functions: Applications to Counting Problems and Recurrence Relations

Generating Functions: Applications to Counting Problems and Recurrence Relations

Divide and Conquer Recurrence Relations and The Master Theorem (Statement and Proof)

Divide and Conquer Recurrence Relations and The Master Theorem (Statement and Proof)

Linear Non homogeneous Recurrence Relations with Constant Coefficients

Linear Non homogeneous Recurrence Relations with Constant Coefficients

Linear Homogeneous Recurrence Relations - General Forms

Linear Homogeneous Recurrence Relations - General Forms

Solving Homogeneous Linear Recurrence Relations - The Fibonacci Sequence

Solving Homogeneous Linear Recurrence Relations - The Fibonacci Sequence

Recursion, Induction and Catalan Numbers

Recursion, Induction and Catalan Numbers

Counting Techniques - Applications to Problem Solving

Counting Techniques - Applications to Problem Solving

Exponential Distribution: Mean and Variance

Exponential Distribution: Mean and Variance

The Pigeonhole Principle: Introduction and Example

The Pigeonhole Principle: Introduction and Example

Merge Sort - Complexity Analysis

Merge Sort - Complexity Analysis

Merge Sort - Introduction and Example

Merge Sort - Introduction and Example

Pick's Theorem: Statement and Proof

Pick's Theorem: Statement and Proof

Arithmetic mean vs Geometric mean

Arithmetic mean vs Geometric mean

The Chinese Remainder Theorem - An example

The Chinese Remainder Theorem - An example

The Wilson's Theorem - Statement and Proof

The Wilson's Theorem - Statement and Proof

Linear Congruences and The Chinese Remainder Theorem

Linear Congruences and The Chinese Remainder Theorem

Prime Factorization is Unique

Prime Factorization is Unique

gcd(a,b) x lcm(a,b) = a x b

gcd(a,b) x lcm(a,b) = a x b

There are an infinite number of primes

There are an infinite number of primes

Modular Arithmetic: ISBN

Modular Arithmetic: ISBN

Greedy Algorithms - Advantages and Limitations

Greedy Algorithms - Advantages and Limitations

Countability and the Set of Rational Numbers

Countability and the Set of Rational Numbers

Telescoping - Simplifying a series

Telescoping - Simplifying a series

The floor function: An example

The floor function: An example

Basic Set Operations through Bit String Representations

Basic Set Operations through Bit String Representations

Proof by contradiction

Proof by contradiction

Proof by contrapositive

Proof by contrapositive

Power Set and its Cardinality

Power Set and its Cardinality

Square root of 3 is irrational

Square root of 3 is irrational

Gamma Distribution: Mean and Variance

Gamma Distribution: Mean and Variance

Gamma function and its integer property

Gamma function and its integer property

Gamma Distribution: Introduction----The PDF integrates to 1

Gamma Distribution: Introduction----The PDF integrates to 1

CDF of a minimum of two random variables

CDF of a minimum of two random variables

Sum of independent Poisson random variables

Sum of independent Poisson random variables

Poisson Random Variable: Variance

Poisson Random Variable: Variance

Poisson Random Variable: Introduction and Expected Value

Poisson Random Variable: Introduction and Expected Value

Sum of independent Geometric/Negative Binomial random variables

Sum of independent Geometric/Negative Binomial random variables

Sum of Independent Binomial Random Variables

Sum of Independent Binomial Random Variables

Negative Binomial Distribution: Variance

Negative Binomial Distribution: Variance

Negative Binomial Distribution: Expected Value

Negative Binomial Distribution: Expected Value

The Negative Binomial Distribution: An Introduction

The Negative Binomial Distribution: An Introduction

A geometric series raised to a power - Relation to the Negative Binomial Distribution

A geometric series raised to a power - Relation to the Negative Binomial Distribution

How many ways can a given sum be obtained using only positive integers

How many ways can a given sum be obtained using only positive integers

Hypergeometric Distribution: Variance

Hypergeometric Distribution: Variance

The Hypergeometric Distribution: Introduction

The Hypergeometric Distribution: Introduction

Vandermonde's Identity - The Hypergeometric Distribution

Vandermonde's Identity - The Hypergeometric Distribution

The Bernoulli and Binomial random variables

The Bernoulli and Binomial random variables

Variance of a sum of random variables

Variance of a sum of random variables

Geometric Random Variable: Variance

Geometric Random Variable: Variance

Summation with squared index

Summation with squared index

Geometric Random Variable: Expected Value (Mean)

Geometric Random Variable: Expected Value (Mean)

Sum of first 'n' positive even numbers

Sum of first 'n' positive even numbers

Sum of first 'n' positive odd numbers

Sum of first 'n' positive odd numbers

Series with increasing factor inside the summation

Series with increasing factor inside the summation

Adding alternate (only even or odd) terms in a binomial series

Adding alternate (only even or odd) terms in a binomial series

Sum of first 'n' positive integers

Sum of first 'n' positive integers