Chapter 01

Chapter 01 - 1.1 Randomness versus determinism 1.2 The...

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Unformatted text preview: 1.1 Randomness versus determinism 1.2 The object of probability 1.3 Approaches to probability 1. Introduction B. Champagne 1 1 Department of Electrical & Computer Engineering McGill University September 1, 2010 ECSE 305 1. Introduction 1.1 Randomness versus determinism 1.2 The object of probability 1.3 Approaches to probability Outline 1.1 Randomness versus determinism 1.2 The object of probability 1.3 Approaches to probability ECSE 305 1. Introduction 1.1 Randomness versus determinism 1.2 The object of probability 1.3 Approaches to probability Determinism in science and engineering Deterministic view in science: provided sufficient information is available about the initial state and operating conditions of a natural process or a man-made system, its future behavior can be predicted exactly. This operational viewpoint has been the prevailing one in most of your college and university education (mechanics, circuit theory, etc.) A typical example is provided by classical mechanics: Consider the motion of a particle under the influence of various forces in three-dimensional space. If we know the initial position and velocity vectors of the particle, its mass and the total force field, Newtons laws can be used to calculate the future trajectory of the particle. ECSE 305 1. Introduction 1.1 Randomness versus determinism 1.2 The object of probability 1.3 Approaches to probability The concept of randomness The above view is idealistic: For most real-life systems or phenomena in science, engineering, and other areas (e.g. games of chance), we cannot do exact predictions. Two basic reasons for this may be identified: Insufficient knowledge of initial state or operating conditions (e.g. motion of electrons in a circuit). Fundamental physical limitations, (e.g. uncertainty principle in quantum physics). We refer to such phenomena or systems as random, in the sense that there is uncertainty about their future behavior: a particular result or situation may or may not occur. The observation of specific quantities derived from such systems/phenomena is called a random experiment ....
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Chapter 01 - 1.1 Randomness versus determinism 1.2 The...

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