Category Archives: Mathematics

Random Variable

Random variable is basically a function which maps from the set of sample space to set of real numbers. The purpose is to get an idea about result of a particular situation where we are given probabilities of different outcomes. See below example for more clarity. Example : Suppose that two coins (unbiased) are tossed… Read More »



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Functions

A function f from A to B is an assignment of exactly one element of B to each element of A (A and B are non-empty sets). A is called Domain of f and B is called co-domain of f. If b is the unique element of B assigned by the function f to the… Read More »



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Discrete Mathematics | The Pigeonhole Principle

Suppose that a flock of 20 pigeons flies into a set of 19 pigeonholes to roost. Because there are 20 pigeons but only 19 pigeonholes, a least one of these 19 pigeonholes must have at least two pigeons in it. To see why this is true, note that if each pigeonhole had at most one… Read More »



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Lagrange’s Mean Value Theorem

Suppose f(x) be a function satisfying three conditions: 1) f(x) is continuous in the closed interval a <= x <= b 2) f(x) is differentiable in the open interval a < x < b   Then according to Lagrange’s Theorem, there exists at least one point ‘c’ in the open interval (a, b) such that:… Read More »



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Eigen Values and Eigen Vectors

Eigen vector of a matrix A is a vector represented by a matrix X such that when X is multiplied with matrix A, then the direction of the resultant matrix remains same as vector X. Mathematically, above statement can be represented as: AX = λX where A is any arbitrary matrix, λ are eigen values… Read More »



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