### 1. Overview

In this article, we’ll discuss the geometric probability distribution and its properties. We will prove each property mathematically and understand its significance. This article assumes basic knowledge of discrete mathematics and algebra for proofs.

### 2. Basic Definitions

We begin with a few basic definitions that will set the stage for things to come.

**Sample space**: A collection or set of discrete points $\Omega$ that is **countable**. A set of values $S$ is said to be countable when there exists a bijection $f: S → A$ where $A$ is a known...

Given an infinite sequence of numbers $<a_0, a_1, a_2, a_3, . . .>$, the (ordinary) generating function for the sequence is defined to be the power series:

$A(x) = \sum_{i=0}^{\infty}a_ix^i = a_0 + a_1x + a_2x^2 + a_3x^3 + . . . $

Consider the binomial expansion of $(1-x)^n$, where $n\in \mathbb{Z}^+$

$(1-x)^n = \sum_{i=0}^{n}\binom{n}{i}(-x)^i$

$= 1 - nx + \frac{n(n-1)}{2!}x^2 – \frac{n(n-1)(n-2)}{3!}x^3 . . . +(-1)^k\frac{n(n-1)(n-2)...(n-k+1)}{k!}x^k . . . + (-1)^nx^n $

Note...

http://discrete.openmathbooks.org/dmoi2/section-27.html

This covers of basics of generating function

And for Recurrence relation

https://www.tutorialspoint.com/discrete_mathematics/discrete_mathematics_recurrence_relation.htm

Hey there,

I’ve found an interactive website to **revise** some mathematics concepts.(For Graph Theory and Probability)

Here ‘s the link: https://mathigon.org/course/graphs-and-networks/introduction

HOPE IT HELPS :)

Information Collected from multiple sources(primarily from Wikipedia, Wolfram Alpha and Narsingh Deo Textbook)

TYPE

Vertex

Edge

Degree

Cycle

Component

Chromatic

Number

Matching, covering and Independent Set

Other

Simple

Undirected

If there is exactly 2 vertices of odd deg then there is a path joins these 2 vertices

Every cut set of a connected...

Day Date Contents Slides Assignments 1 Sep 14 Introduction to probability- simple problems- Rolling a die n times and find the probability of getting at least one six,

probability of forming two men and two women out of four people Lecture Notes - Best one 2 Sep 17 Class Test- 5 Questions: Time-15 minutes

**Problems**

1. 3 men and 3 women are to be seated (i) In a row of chairs...

**SET THEORY AND ALGEBRA**Day Date Contents Slides Assignments 1 July 2 No discussion Assignment 1 2 July 3 Introduction to Sets, Relations, Functions 3 July 4 Equivalence Relations, Types of Functions Assignment 2 July 5 No Discussion: Problem solving from...

**Important Questions:**

http://gateoverflow.in/questions/mathematics/discrete-mathematics/graph-theory?sort=featured

**More Questions:**

Some Good Questions useful for GATE