UNIT 2 THEOREMS Structure 2.1 Introduction Objectives PROBABILITY 2.2 Some Elementary Theorems 2.3 General Addition Rule 2.4 Conditional Probability and Independence 2.4.1 Conditional Probability 2.4.2 Independent Events and MultiplicationRule 2.4.3 Theorem of Total Probability and Bayes Theorem 2.5 Summary 2.1 INTRODUCTION You have already learnt about probability axioms and ways to evaluate probability of events in some simple cases. In this unit‚ we discuss ways to evaluate
Premium Probability theory Conditional probability
pressure dynamics specified by Bernoulli’s Principle to keep their rare wheels on the ground‚ even while zooming off at high speed. It is successfully employed in mechanism like the carburetor and the atomizer. The study focuses on Bernoulli’s Theorem in Fluid Application. A fluid is any substance which when acted upon by a shear force‚ however small‚ cause a continuous or unlimited deformation‚ but at a rate proportional to the applied force. As a matter of fact‚ if a fluid is moving horizontally
Premium Fluid dynamics Energy Force
How We Use the Pythagorean Theorem in Everyday Life First‚ let’s discuss the inventor of the theorem before how we use it. Pythagoras of Samos is a very odd fellow but is very well known despite not have written anything in his lifetime so what we know about him comes from Historians and Philosophers. Though we know he was a Greek philosopher and mathematician mainly known for the Pythagorean Theorem that we all learned in 6th grade. (a2 + b2 = c2). His theorem states that that the square of
Premium Pythagorean theorem Angle Mathematics
The Coase Theorem In “The Problem of Social Cost‚” Ronald Coase introduced a different way of thinking about externalities‚ private property rights and government intervention. The student will briefly discuss how the Coase Theorem‚ as it would later become known‚ provides an alternative to government regulation and provision of services and the importance of private property in his theorem. In his book The Economics of Welfare‚ Arthur C. Pigou‚ a British economist‚ asserted that the existence
Premium Externality Market failure Welfare economics
The assignment for the week is on page 371 number 98. We will be using Pythagorean Theorem‚ quadratic‚ zero factor‚ and compound equation‚ to solve this equation. We will explain step by step to solve how many paces to reach Castle Rock for Ahmed and Vanessa had to accomplish to meet there goal. Ahmed has half of a treasure map‚ which indicates that the treasure is buried in the desert 2x + 6 paces from Castle Rock. Vanessa has the other half of the map. Her half indicates that to find the treasure
Premium Pythagorean theorem Mathematics Triangle
Taylors Theorem: Taylor’s theorem gives an approximation of a n times differentiable function around a given point by a n-th order Taylor-polynomial. For analytic functions the Taylor polynomials at a given point are fixed order truncations of its Taylor’s series‚ which completely determines the function in some locality of the point. There are numerous forms of it applicable in different situations‚ and some of them contain explicit estimates on the approximation error of the function by its Taylor-polynomial
Premium Series Function
------------------------------------------------- Polynomial long division From Wikipedia‚ the free encyclopedia In algebra‚ polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree‚ a generalised version of the familiar arithmetic technique called long division. It can be done easily by hand‚ because it separates an otherwise complex division problem into smaller ones. Sometimes using a shorthand version called synthetic division is
Premium Field Polynomial Division
BINOMIAL THEOREM : AKSHAY MISHRA XI A ‚ K V 2 ‚ GWALIOR In elementary algebra‚ the binomial theorem describes the algebraic expansion of powers of a binomial. According to the theorem‚ it is possible to expand the power (x + y)n into a sum involving terms of the form axbyc‚ where the coefficient of each term is a positive integer‚ and the sum of the exponents of x and y in each term is n. For example: The coefficients appearing in the binomial expansion are known as binomial coefficients.
Premium
Thevenin Theorem It provides a mathematical technique for replacing for a given network‚ as viewed from two output terminals by a single voltage source with a series resistance. It makes the solution of complicated networks (particularly‚ electronic networks) quite quick and easy. The Thevenin’s theorem‚ as applied to d.c. circuits‚ may be stated as under: The current flowing through a load resistance RL connected across any two terminals A and B of a linear‚ active bilateral network is given
Premium Electrical resistance Ohm's law Voltage
Stokes’ theorem In differential geometry‚ Stokes’ theorem (or Stokes’s theorem‚ also called the generalized Stokes’ theorem) is a statement about the integration of differential forms on manifolds‚ which both simplifies and generalizes several theorems from vector calculus. The general formulation reads: If is an (n − 1)-form with compact support on ‚ and denotes the boundary of with its induced orientation‚ and denotes the exterior differential operator‚ then. The modern Stokes’ theorem is a
Premium