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# chap01 - 1 Chapter 1 Introduction 1.1 Randomness versus...

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1 Chapter 1 Introduction 1.1 Randomness versus determinism 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, Newton’s laws can be used to calculate (i.e. predict) the future trajectory of the particle. c ± 2003 Benoˆ ıt Champagne Compiled January 11, 2012

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1.1 Randomness versus determinism 2 The concept of randomness: The above view is highly idealistic: In most ”real-life” scientiﬁc and engineering problems, as well as many other situations of interest (e.g. games of chance), we cannot do exact predictions about the phenomena or systems under consideration. Two basic reasons for this may be identiﬁed: - we do not have suﬃcient knowledge of the initial state of the system or the operating conditions (e.g. motion of electrons in a micropro- cessor circuit). - due to fundamental physical limitations, it is impossible to make exact predictions (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 a random system or phenomenon is often referred to as a random experiment. c ± 2003 Benoˆ ıt Champagne Compiled January 11, 2012
1.1 Randomness versus determinism 3 Examples: Consider the following game of chance: - We roll an ordinary six-sided die once and observe the number show- ing up, also called outcome.

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## This note was uploaded on 02/12/2012 for the course ECSE 305 taught by Professor Champagne during the Spring '09 term at McGill.

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chap01 - 1 Chapter 1 Introduction 1.1 Randomness versus...

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