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Unformatted text preview: 1 Introduction • Experiment • Random • Random experiment1 Introduction1 Introduction1 Introduction1 Introduction2 Random Variables • In an experiment, a measurement is usually denoted by a variable such as X . • In a random experiment , a variable whose measured value can change (from one replicate of the experiment to another) is referred to as a random variable .2 Random Variables3 Probability • Used to quantify likelihood or chance • Used to represent risk or uncertainty in engineering applications • Can be interpreted as our degree of belief or relative frequency3 Probability • Probability statements describe the likelihood that particular values occur. • The likelihood is quantified by assigning a number from the interval [0, 1] to the set of values (or a percentage from 0 to 100%). • Higher numbers indicate that the set of values is more likely.3 Probability • A probability is usually expressed in terms of a random variable. • For the part length example, X denotes the part length and the probability statement can be written in either of the following forms • Both equations state that the probability that the random variable X assumes a value in [10.8, 11.2] is 0.25.3 Probability Complement of an Event • Given a set E , the complement of E is the set of elements that are not in E . The complemen t is denoted as E ’ . Mutually Exclusive Events • The sets E 1 , E 2 ,..., E k are mutually exclusive if the intersection of any pair is empty. That is, each element is in one and only one of the sets E 1 , E 2 ,..., E k .3 Probability Probability Properties3 Probability Events • A measured value is not always obtained from an experiment. Sometimes, the result is only classified (into one of several possible categories). • These categories are often referred to as events . Illustrations • The current measurement might only be recorded as low, medium, or high ; a manufactured electronic component might be classified only as defective or not; and either a message is sent through a network or not. 4 Continuous Random Variables 34.1 Probability Density Function • The probability distribution or simply distribution of a random variable X is a description of the set of the probabilities associated with the possible values for X .4 Continuous Random Variables 34.1 Probability Density Function4 Continuous Random Variables 34.1 Probability Density Function4 Continuous Random Variables 34.1 Probability Density Function4 Continuous Random Variables 34.1 Probability Density Function4 Continuous Random Variables...
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 Spring '10
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